Question

prove the following identity.
sin^4theta-cos^4theta=1-2cos^2theta​

Answer 1

Answer:

To Prove:sin⁴x - cos⁴x = 1- 2sin²x.cos²x

Step-by-step explanation:

Solving LHS:

= (sin²x-cos²x)² [ (a-b)²=a²+b²-2ab]

= sin⁴x + cos⁴x - 2sin²x.cos²x [sin²x+cos²x = 1]

= 1- 2sin²x.cos²x

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