Prove that ` sin^2alpha-sin^4alpha= cos^2alpha-cos^4alpha`

If (cos^(4)alpha)/(cos^(2) beta) + (sin^(4)alpha)/(sin^(2)beta) = 1, prove that sin^(4)alpha + sin^(4) beta = 2 sin^(2) alpha sin^(2) beta

If f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then

If x sin ^3 alpha + y cos^3 alpha = sin alpha cos alpha and x sin alpha - y cos alpha =0 , then x^2 +y^2 is

x=sqrt(a^2cos^2alpha+b^2sin^2alpha)+sqrt(a^2sin^2alpha+b^2cos^2alpha) then x^2=a^2+b^2+2sqrt(p(a^2+b^2)-p^2) , where p is equal to (a) a^2cos^2alpha+ b^2sin^2alpha (b) a^2sin^2alpha+b^2cos^2alpha (c) (1/2)(a^2+b^2+(a^2-b^2)cos2alpha) (d) (1/2)(a^2+b^2-(a^2-b^2)cos2alpha)

If cot^3alpha+cot^2alpha+cotalpha=1 then (a) cos2alpha.tanalpha=-1 (b) cos2alpha.tanalpha=1 (c) cos2alpha-tan2alpha=1 (d) cos2alpha-tan2alpha=-1

For alpha=pi/7 which of the following hold(s) good? (a) tanalphatan2alphatan3alpha=tan3alpha-tan2alpha-tanalpha (b) cos e calpha=cos e c2alpha+cos e c4alpha (c) cosalpha-cos2alpha+cos3alpha=1/2 (d) 8cosalphacos2alphacos4alpha=1

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha

If cos^(-1)x-cos^(-1)y/2=alpha,t h e n4x^2-4x ycosalpha+y^2 is equal to (a)4 (b) 2sin^2alpha (c) -4sin^2alpha (d) 4sin^2alpha

IF tan alpha = ( sin alpha - cos alpha )/( sin alpha + cos alpha) , then sin alpha + cos alpha is

Prove that sin 4alpha = 4 tan alpha (1 - tan^(2) alpha)/((1 + tan^(2) alpha)^(2))