Question

(7) prove that
sin⁴x- cos⁴x= 1 - 2cos²x
​

Answer 1

Step-by-step explanation:

sin⁴x- cos⁴x= (sin²x-cos²x)(sin²x+cos²x)

=> 1(sin²x-cos²x)

=> (1-cos²x-cos²x)

=> (1-2cos²x)

Hence Proved.

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Answer 2

Explanation:

LHS= sin⁴x-cos⁴x

= (sin²x)²-(cos²x)²

= (sin²x+cos²x)(sin²x-cos²x)

sin²x+cos²x= 1

= 1 × (1-cos²x-cos²x)

= 1- 2 cos²x

= RHS

Hope it helps u.....