Question

Which expression is equal to the example?

Answer 1

$1-(cosx)^4$ value is $2sin^4-sin^4x$ . Correct option is D) $2sin^4-sin^4x$ .

Step-by-step explanation:

Here we have , expression to evaluate:

$1-(cosx)^4$

⇒ $1-((cosx)^2)^2$

⇒ $1-(1-(sinx)^2)^2$

We know that , $sin^2x = 1-cos^2x$ , putting value in equation $1-(1-(sinx)^2)^2$

⇒ $1-(1+sin^4x-2sin^4)$

⇒ $1-1-sin^4x+2sin^4$

⇒ $-sin^4x+2sin^4$

⇒ $2sin^4-sin^4x$

Therefore , $1-(cosx)^4$ value is $2sin^4-sin^4x$ . Correct option is D) $2sin^4-sin^4x$