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Trigonometric, Identities & Formulas
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Relation between angle and sides of the triangle, values of trigonometric functions at standard angles, transformation and trigonometric identities
Sona 
Chandi 
Tole 
Pandit 
Badri 
Parsad 
Har 
Har 
Bole 
sin Î¸ 
cos Î¸ 
tan Î¸ 
P 
B 
P 
H 
H 
B 
cosec Î¸ 
sec Î¸ 
cot Î¸ 
0^{o} 
30^{o} 
45^{o} 
60^{o} 
90^{o} 

Sin 
0 
1/2 
\[\frac{1}{\sqrt{2}}\] 
\[\frac{\sqrt{3}}{2}\] 
1 
Cos 
1 
\[\frac{\sqrt{3}}{2}\] 
\[\frac{1}{\sqrt{2}}\] 
1/2 
0 
Tan 
0 
\[\frac{1}{\sqrt{3}}\] 
1 
\[\sqrt{3}\] 
\[\infty\] 
Cot 
\[\infty\] 
\[\sqrt{3}\] 
1 
\[\frac{1}{\sqrt{3}}\] 
0 
sec 
1 
\[\frac{2}{\sqrt{3}}\] 
\[\sqrt{2}\] 
2 
\[\infty\] 
cosec 
\[\infty\] 
2 
\[\sqrt{2}\] 
\[\frac{2}{\sqrt{3}}\] 
1 
Sin0^{o} 
Sin30^{o} 
Sin45^{o} 
Sin60^{o} 
Sin90^{o} 
0 
1 
2 
3 
4 
\[\frac{0}{4}\] 
\[\frac{1}{4}\] 
\[\frac{2}{4}\] 
\[\frac{3}{4}\] 
\[\frac{4}{4}\] 
0 
\[\frac{1}{4}\] 
\[\frac{1}{2}\] 
\[\frac{3}{4}\] 
1 
\[\sqrt{0}\] 
\[\sqrt{\frac{1}{4}}\] 
\[\sqrt{\frac{1}{2}}\] 
\[\sqrt{\frac{3}{4}}\] 
\[\sqrt{1}\] 
0 
\[\frac{1}{2}\] 
\[\frac{1}{\sqrt{2}}\] 
\[\frac{\sqrt{3}}{2}\] 
1 
For values of other trigonometric ratios
write all these values for sinÎ¸ in the reverse order(from right to left)
Derivation of Sin^{2}Î¸ + cos^{2}Î¸ = 1
Let us take an right angled triangle ABC as shown belowIn triangle
ABC, by Pythagoras theorem
AB^{2} = AC^{2} + BC^{2} ................ (1)
Dividing on both side by AB^{2}
Derivation of cosec^{2}Î¸  cot^{2}Î¸ = 1
Derivation of Sec^{2}Î¸  tan^{2}Î¸ = 1
Geometrical Representation of Trigonometric Ratios with the 60^{o} .
Geometrical Representation of Trigonometric Ratios with the 45^{o}.
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Comments
Good and very useful.
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