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` .

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`