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Math Assignment Class XI Ch-3 | Trigonometric Functions

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.



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

Question 5

Prove the followings

  i)   cos24o + cos 55o + cos 125o + cos 204o + cos 300o = 1/2

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


Question 6:   Simplify  

Ans: 1

 Solution Hint:

Question 7

Evaluate the following :

Question 8

Prove that : tan70o = tan20o + 2tan50o

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 α 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  α are  p and q, Then

ATQ :  p + q = α,  p – q = x,  

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

Question 13

Prove that :   cos20o cos40o cos60o cos80o = 1/16

Question 14  

Prove that :   sin20o sin40o sin60o sin80o = 3/16

Question 15

Prove That : 

Solution Hint : 

Use tan θ = sin θ/cos θ, then using AB and CD formulas

Question 16

If cos(θ + 2 α) = n cos θ , 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 sin18o  



θ = 18o   5 θ = 90o     2 θ + 3 θ = 90o    2 θ = 90o - 3 θ

Now taking sin on both side we get

Sin (2 θ) = Sin (90o - 3 θ)    Sin (2 θ) = Cos (3 θ)

2Sin θ cos θ = 4Cos3 θ – 3cos θ     2Sin θ  = 4Cos2 θ – 3

2Sin θ  = 4(1-sin2 θ) – 3

4 sin2 θ + 2sin θ – 1 = 0

Now using quadratic formula here and find the value of sin θ

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



Question 24

Prove that:   
Solution Hint: Apply AB formulas

Question 25

If tan35o = α , then find the value of      in terms of α 


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 = 45o 

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 45o  ⇒ x + y = 45o

Question: 30

Prove that: Cos6θ = 32cos6 θ - 48cos4 θ + 18cos2 θ - 1

Solution Hint: Use cos6θ = cos3(2θ) = - 3cos2θ + 4cos3 2θ and then proceed.

Question: 31

Prove that: cos6x = 1 - 18sin2x + 48sin4x - 32sin6x

Solution Hint: Use cos6θ = cos3(2θ) =  -3cos2θ + 4cos3 2θ .

Now putting cos2θ = 1 - 2sin2θ we get

cos6θ = -3(1 - 2sin2θ) + 4(1 - 2sin2θ)3

Solving this we get the required result

Question 32

Prove that:  

Solution Hint

Using tanθ = sinθ/cosθ 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 sin2θ = 2sinθcosθ in the numerator for two times.

Question: 33

Prove that:  sin3x cos3x + cos3xsin3x =  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  


Question: 36

Prove that: sin2α + sin2(α - β) - 2sinα cosβ sin(α - β) = sin2β

Solution Hint: 

LHS = sin2α + sin2(α - β) - [sin(α + β) + sin(α - β)]sin(α - β)

        = sin2α + sin2(α - β) - sin(α + β)sin(α - β) - sin2(α - β)

        = sin2α - [sin2α - sin2β] ..... [Using sin(A+B)sin(A-B) = sin2A - sin2B ]

        = sin2β

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 :    


Solution Hint: 

Taking "-" common from numerator

Using the formula:    

Question 39 : Prove that


Solution Hint:

Using this formula: sin3x = 3sinx – 4sin3x  



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



General Solutions of Trigonometric Functions
These questions are deleted from the CBSE syllabus 

Question 39

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

Question 40


Question 41

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

Question 42


Question 43


Solution  Hint: 



Question 44


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 cos2x + 3 sin x = 0.

Question 46

Find general solution of cos2x cosec x + 3sinx + 3 = 0

Ans:  ,   

Solution Hint: 

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

Solve the quadratic equations.

PDF view of the assignment



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