if `cos^2theta= (m^2-1)/3 and tan^3\ theta/2 = tanalpha,` prove that `cos^(2//3) alpha+ sin^(2//3) alpha= (2/m)^(2//3)`

If tan theta = (1)/( sqrt(3)) , prove that 7 sin^(2) theta + 3 cos ^(2) theta = 4

sin alpha-cos alpha=m, show that : sin^(3)alpha-cos^(3)alpha=(3m-m^(3))/(2).

If tan theta=(sin alpha-cos alpha)/(sin alpha+cos alpha), prove that 2cos^(2)theta=1+sin2 alpha

(i) tan3 theta tan7 theta + 1 = 0 (ii) sin ^ (2) theta = sin ^ (2) alpha

If a cos^(2)theta+3a cos theta sin^(2)theta=m and a sin^(3)theta+3a cos^(2)theta sin theta=n ,then prove that: (m+n)^(2/3)+(m-n)^(2/3)=2a^(2/3)

General term ( sin^2 theta = sin^2 alpha , cos^2 theta = cos^2 alpha, tan^2 theta= tan^2 alpha)

If a cos^(3)alpha+3a cos alpha*sin alpha=m and a sin^(3)alpha+3a cos^(3)alpha sin^(3)alpha=n then (m+n)^((2)/(3))+(m-n)^((2)/(3))

If tanalpha=2 , then the value of (sinalpha)/(sin^(3)alpha+cos^(3)alpha) is

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .

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