Question

How to know which identity should be used when ?

class10

Answer 1

Answer :

It's depend on your question and your practise on trigonometric equations , and we can use these identities as per required in question ,

Sin $\theta$ = $\frac{Opposite}{Hypotenuse}$

Sin $\theta$ = $\frac{1}{Cosec\theta }$

Cos $\theta$ = $\frac{Adjacent}{Hypotenuse}$

Cos $\theta$ = $\frac{1}{Sec\theta }$

tan $\theta$ = $\frac{Opposite}{Adjacent}$

tan $\theta$ = $\frac{1}{Cot\theta }$

Here are some identities

Sin ² ​$\theta$ + Cos ² ​$\theta$ = 1
And
Sec ² ​$\theta$ - tan ² ​$\theta$ = 1

Sin ( A + B ) = Sin A Cos B + Cos A Sin B
Sin ( A - B ) ​= Sin A Cos B - Cos A Sin B

Cos ( A + B ) = Cos A Cos B - Sin A Sin B

Cos ( A - B ) = Cos A Cos B + Sin A Sin B

tan ( A + B ) = $\frac{\tan A\hspace{0.17em}+\hspace{0.17em}\tan B}{1-\tan A\hspace{0.17em}\tan B}$

tan ( A - B ) = $\frac{\tan A\hspace{0.17em}-\hspace{0.17em}\tan B}{1+\tan A\hspace{0.17em}\tan B}$

Sin 2A = 2 SinA cos A

Cos 2A = Cos² A - Sin² A

tan 2A = $\frac{2\tan A}{1-{\tan }^{2}A}$