Question

Please solve q 18 ?

Answer 1

The correct answer is option `(B)`

Explanation:

If

`sinx+sin^2x+sin^3x=1`

Then

`=>sinx+sin^3x=1-sin^2x`

`sinx+sin^3x=cos^2x`

Squaring both sides

`=>(sinx+sin^3x)^2=(1-sin^2x)^2`

`=>sin^2x+sin^6x+2sin^4x=cos^4x`

#=> 1-cos^2x+(1-cos^2x)^3+2(1-cos^2x)^2=cos^4x#

#=> 1-cos^2x+1-3cos^2x+3cos^4x-cos^6x+2-4cos^2x+2cos^4x=cos^4x#

`=>cos^6x-4cos^4x+8cos^2x=4`

`cos^6x+8cos^2x=4+4cos^4x`

The correct answer is option `(B)`

https://socratic.org/questions/sinx-sin-x-sin-3x-1-the-what-is-cos-6x-4cos-4x-8cos-2x