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### Math Assignment Class XI Ch-3 | Trigonometric Functions

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**Math Assignment | Class XI | Chapter 3 **

** Trigonometric Functions**

**Extra questions of chapter 3 class 11 Trigonometric Functions with answer and hints to the difficult questions. Important and useful math. assignment for the students of class 11**

**For better results**

**Students should learn all the basic points of Trigonometry up to 11th standard****Student should revise NCERT book thoroughly with examples.****Now revise this assignment. This assignment integrate the knowledge of the students.**

**ASSIGNMENT FOR XI STANDARD TRIGONOMETRY**

**STRICTLY ACCORDING TO THE CBSE AND DAV BOARD**

**Question 1**

**Find the degree measure for the following radian measure**

**Question 2**

**Find the radian measure for the following degree measure**

**Question 3**

**Find the magnitude, radian and degree, of the interior angles of a regular**

**Solution Hint:**

**Note: Each interior angle of a regular polygon is given by : **

** Where n is the number of sides.**

**Question 4**

**If sin Î¸ =12/13 and Î¸ lie in the second quadrant, then find the value of ****sec Î¸**** + tan Î¸. Ans. [- 5]**

**Question 5**

**Prove the followings**

** i) cos24 ^{o} + cos 55^{o} + cos 125^{o} + cos 204^{o} + cos 300^{o} = 1/2**

**ii) sin 600 ^{o} tan(-690^{o}) + sec 840^{o} cot(-945^{o}) = 3/2**

**iii) **

**Question 6: Simplify**

**Ans: 1**

** Solution Hint:**

**Question 7**

**Evaluate the following :**

**Question 8**

**Prove that : tan70 ^{o} = tan20^{o} + 2tan50^{o}**

**Solution Hint:**

**Now cross-multiply and simplify the above fraction we get the required result.**

**Question 9**

**Question 10**

** If tan A = k tan B, then show that: **

**Solution Hint: tan A = k tan B**

** ****Now apply componendo and dividendo and using trigonometric formulas.**

**Question 11**

**If tan(A + B) = p, tan(A – B) = q, then show that : **

**Solution Hint: **

**Start from RHS and then putting the value of p and q then simplify and get the result.**

**Question 12**

**An angle ****Î±**** is divided into two parts such that the ratio of the tangents of the two parts = k and difference of two parts = x then show that: **

**Solution hint:**

**Let two parts of Î±**** are p and q, Then**

**ATQ : p + q = Î±, p – q = x, **

**Now applying componendo and dividendo and simplify we get the required result.**

**Question 13**

**Prove that : cos20 ^{o} cos40^{o} cos60^{o} cos80^{o} = 1/16**

**Question 14**

**Prove that : sin20 ^{o} sin40^{o} sin60^{o} sin80^{o} = 3/16**

**Question 15**

**Prove That : **

**Solution Hint : **

**Use tan**** Î¸**** = sin Î¸/cos Î¸, then using AB and CD formulas**

**Question 16**

**If cos(Î¸ + 2 Î±) = n cos Î¸ , then prove that : **

**Solution Hint: **

**Applying componendo and dividendo then applying CD formulas then simplify the fractions we get the required result.**

**Question 17**

** ****Prove that: **

**Solution Hint**

**Taking LHS and convert these into cosine functions.**

**Multiply and divide by 2 and the apply AB formulas**

**Question 18**

**Prove that: **

**Solution Hint:**

**Multiply and divide by 2 and then apply AB formulas**

**Question 19**

**Find the value of sin18 ^{o }**

**Ans: **

**Solution:**

**Î¸ = 18 ^{o} ⇒ 5 Î¸ = 90^{o} ⇒ 2 Î¸ + 3 Î¸ = 90^{o} ⇒ 2 Î¸ = 90^{o} - 3 Î¸**

**Now taking sin on both side we get**

**Sin (2 Î¸) = Sin (90 ^{o} - 3 Î¸) Sin (2 Î¸) = Cos (3 Î¸)**

**2Sin Î¸ cos Î¸ = 4Cos ^{3} Î¸ – 3cos Î¸ 2Sin Î¸ = 4Cos^{2} Î¸ – 3**

**2Sin Î¸ = 4(1-sin ^{2} Î¸) – 3**

**4 sin ^{2} Î¸ + 2sin Î¸ – 1 = 0**

**Now using quadratic formula here and find the value of sin Î¸**

**Question 20**

**Prove that : **

**Solution Hint:**

** **

**Question 21**

**i) Evaluate: **

**Solution Hint: Using: **

**ii) Evaluate: **

**Question 22**

**Prove that: **

**Solution Hint:**

**Multiply numerator and denominator by 2**

**Applying AB formulas we get**

**Now applying CD formulas we get the required result.**

**Question 23**

** ****Find , and , when tan x = , and x lie in II quadrant**

**Ans: **** **

** , **

**Question 24**

**Prove that:**

**Solution Hint: Apply AB formulas**

**Question 25**

**If tan35 ^{o} = Î± , then find the value of in terms of Î± **

**Ans: **

**Question 26**

**Prove that : **

**Question: 27**

**Prove that : **

**Solution Hint:**

**Use formula: **

**Now simplify and then apply CD formula we get the required result**

**Question 28**

**Prove that: **

**Question 29**

**If tan x + tan y + tan x tan y = 1, find (x + y).**

**Ans: x + y = 45 ^{o} **

**Solution Hint:**

**tan x + tan y = 1-tan x tan y**

**Dividing on both side by 1-tanx tany we get**

**tan(x + y) = tan 45 ^{o} ⇒ x + y = 45^{o}**

**Question: 30**

**Prove that: Cos6Î¸ = 32cos ^{6} Î¸ - 48cos^{4} Î¸ + 18cos^{2} Î¸ - 1**

**Solution Hint: Use cos6Î¸ = cos3(2Î¸) = - 3cos2Î¸ + 4cos ^{3} 2Î¸ and then proceed.**

**Question: 31**

**Prove that: cos6x = 1 - 18sin ^{2}x + 48sin^{4}x - 32sin^{6}x**

**Solution Hint: Use cos6Î¸ = cos3(2Î¸) = -3cos2Î¸ + 4cos ^{3} 2Î¸ .**

**Now putting cos2****Î¸ = ****1 - 2sin ^{2}Î¸ we get**

**cos6****Î¸ = -3(****1 - 2sin ^{2}Î¸) + **

**4(1 - 2sin**

^{2}Î¸)^{3}**Solving this we get the required result**

**Question 32**

**Prove that: **

**Solution Hint**

**Using tanÎ¸ = sinÎ¸/cosÎ¸ in numerator and in denominator**

**Taking LCM then using the formula sin(A+B) and sin (A-B) in numerator and in denominator respectively.**

**Now using sin2Î¸ = 2sinÎ¸cosÎ¸ in the numerator for two times.**

**Question: 33**

**Prove that: sin3x cos ^{3}x + cos3xsin^{3}x = sin4x**

**Solution Hint: Expand sin3x and cos3x**

**Now multiply and divide by 2**

**Applying 2sinxcosx = sin2x for two times we get the required result.**

**Question 34**

**Prove that : **

**Solution : **

**Question 35**

**Evaluate: and **

**Solution:**

**Question: 36**

**Prove that: sin ^{2}Î±
+ sin^{2}(Î± - Î²) - 2sinÎ± cosÎ² sin(Î± - Î²) = sin^{2}Î²**

**Solution Hint: **

**LHS = sin ^{2}Î± + sin^{2}(Î± - Î²) - [sin(Î± + Î²) + sin(Î± - Î²)]sin(Î± - Î²)**

** = sin ^{2}Î± + sin^{2}(Î± - Î²) - sin(Î± + Î²)sin(Î± - Î²) - sin^{2}(Î± - Î²)**

** = sin ^{2}Î± - [sin^{2}Î± - sin^{2}Î²] ..... [Using sin(A+B)sin(A-B) = sin^{2}A - sin^{2}B ]**

** = sin ^{2}Î²**

**Question 37**

**If , then find the value of xy + yz + zx **

**Answer 0**

**Solution Hint:**

**Let all equations = k**

**Now find the value of x, y, z in terms of k**

**Now find the value of , it should be '0'**

**Putting this value in xy + yz + zx = **

** = **

** = xyz ×0 = 0**

**Question 38**

**Find the value of : **

**Ans: **

**Solution Hint: **

**Taking "-" common from numerator**

**Using the formula: **

**Question 39 : Prove that**

**Solution Hint:**

Using this formula: sin3x
= 3sinx – 4sin^{3}x

Using C, D formulas for the middle two terms we get

**Question 39**

**Find the general solution of the equation: cos x + cos 2x + cos 3x = 0.**

**Question 40**

**Solve: **

**Question 41**

**Solve the equation: sin 3x + sin 5x + sin 7x = 0, **

**Question 42**

**Solve: **

**Question 43**

**Solve: **

**Solution Hint: **

** **

** **

**Question 44**

**Solve: **

**Solution Hint: **

** **

**Dividing on both side by **

** i.e. by 2 **

Now proceed this question as previous one.

**Question 45**

**Find the general solution of: 2 cos ^{2}x + 3 sin x = 0.**

**Question 46**

**Find general solution of cos ^{2}x cosec x + 3sinx + 3 = 0**

**Ans: , **

**Solution Hint: **

**Convert all terms into sin x , we get a quadratic equation.**

**Solve the quadratic equations.**

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