Question

cos4A=1-8sin²A.cos²A​

Answer 1

To Prove -

→ Cos 4A = 1 - 8 sin²A . cos²A.

Solution -

Taking LHS -

→ Cos 4A = Cos 2(2A) .

Cos 2 theta = 1 - 2sin² theta.

→ 1 - 2 sin² 2A

→ 1 - 2 [ sin 2A] ²

Sin 2A = 2 Sin A Cos A

→ 1 - 2 [ 2 Sin A . cos A ]²

→ 1 - 2 [ 4 Sin²A. Cos²A]

→ 1 - 8 Sin²A. Cos ²A .

LHS = RHS .

Hence proved

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Other identities -

→ Cos 2x = cos²x - sin²x

→ Cos 2x = 2 cos²x - 1

→ tan 2x = 2tanx/ 1- tan²x

→ Sin 2x = 2tanx/1+ tan²x

→ Cos 2x = 1-tan²x/1+tan²x

Answer 2

The answer of ur question (See in attachment)