Question

Help plzz!! Are all these identities correct? Check them

Answer 1

Yes all are correct except a minor error in second one. cos 2A = 2cos² A - 1

1. sin 2A = 2sin A. cos A = 2tan A/ 1 + tan²A

2. cos 2A = cos² A - sin² A = 1 - 2sin² A = 2cos² A - 1 = 1 - tan² A / 1 + tan² A

3. sin 3A =
sin [A + 2A] = sin 2A . cos A + cos 2A . sin A
= 2 sin A cos A cos A + cos 2A sin A
= 2 sin A [ 1 - sin² A]  + [1 - 2 sin² A] sin A
= 2 sin A - 2 sin A³ + sin A - 2 sin³ A
= 3 sin A - 4 sin³A

4. cos 3A =
cos [ A+ 2A] = cos 2A Cos A - sin 2A sin A
= [ 2cos² A - 1] cos A  - [2 sin A cos A] sinA
= 2 cos³ A - cos A - 2 sin² A cos A
= 2 cos³ A - cos A - 2[ 1 - cos² A] cos A
= 2 cos³ A - cos A - 2cos A + 2cos² A cos A
= 2 cos³ A - 3cos A + 2 cos³ A
= 4 cos³ A - 3 cos A

Hope This Helps You

Answer 2

Hey there! 

Bellastark has already answered you, but still, since there's one answer slot remaining, I would like to answer. 

Every identity in the given image is correct except for one in the 2nd one.

You've written cos2A = cos²A - 1 
But, it is cos2A = 2cos²A - 1 

Some more helpful identities :

sin(α + β) = sin(α) cos(β) + cos(α) sin(β)

sin(α – β) = sin(α) cos(β) – cos(α) sin(β)

cos(α + β) = cos(α) cos(β) – sin(α) sin(β)

cos(α – β) = cos(α) cos(β) + sin(α) sin(β)