If `sinx+cosx=a`, then prove that: `sin^6x+cos^6x=1-3/4(a^2-1)^2`where`a^2<=2`

Similar Questions

Explore conceptually related problems

If sin x+cos x=a then prove that: sin^(6)x+cos^(6)x=1-(3)/(4)(a^(2)-1)^(2), where a^(2)<=2

Prove that, sin^(6)x + cos^(6)x = 1-3/4 sin^(2) 2x.

If sinx+ sin^2x =1 , then cos^8x+ 2cos^6x +cos^4x =

Prove that, (sinx+cosx)^2=1+sin2x

Prove that sin^(6)x + cos^(6)x = 1 - 3 sin^(2) x cos^(2)x .

If sin theta+cos theta=x then prove that sin^(6)theta+cos^(6)theta=(4-3*(x^(2)-1)^(2))/(4)

If sin theta+cos theta=x, Prove that :sin^(6)theta+cos^(6)theta=(4-3(x^(2)-1)^(2))/(4)

Prove that: cos^2 2x-cos^2 6x=sin4xsin8x

If sinx+sin^2x=1. then evaluate : (i) cos^8x+2cos^6x+cos^4x

prove that [2(sin^3 x - cos^3 x )/(sinx -cosx)]-sin2x=2