Question

If sin theta + tan theta+ sin cube theta = 1 prove that cos2theta - 4cos4 theta + 8 cos2theta

Answer 1

$\mathfrak{The\:Answer\:is}$


Givensinθ+(sinθ)^2+(sinθ)^3=1
=>sinθ+(sinθ)^3=(cosθ)^2
=>(sinθ)^2+2(sinθ)^4+(sinθ)^6=(cosθ)^4
=>1-(cosθ)^2+2(1-2(cosθ)^2+(cosθ)^4)+(1-3(cosθ)^2+3(cosθ)^4-(cosθ)^6)=(cosθ)^4
=>(cosθ)^6-4(cosθ)^4+8(cosθ)^2=4.


$\boxed{Hope\:This\:Helps}$