Please solve q18 ?

enter image source here

1 Answer
May 2, 2018

#rarrcos^6x+8cos^2x=4+4cos^4x#

Explanation:

#rarrsinx+sin^2x+sin^3x=1#

#rarrsinx(1+sin^2x)=1-sin^2x=cos^2x#

#rarrsin^2x(1+2sin^2x+sin^4x)=cos^4x#

#rarrsin^2x(1+2sin^2x+(1-cos^2x)^2)=cos^4x#

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

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

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

#rarr4-4cos^2xcancel(+cos^4x)-4cos^2x+4cos^4x-cos^6x=cancelcos^4x#

#rarrcos^6x+8cos^2x=4+4cos^4x#