Prove that `sin4 alpha=4tan alpha (1- tan^(2)alpha)/((1+tan^2 alpha)^2`

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

Prove that tan(alpha-beta)=(tanalpha-tanbeta)/(1+tanalphatanbeta)

Prove that tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)

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

prove that : tan(alpha)+2 tan(2alpha) +4(tan4alpha)+8cot(8alpha) = cot(alpha)

If vector vec b=(t a nalpha,-1, 2sqrt(sinalpha//2))a n d vec c=(t a nalpha, t a nalpha, 3/(sqrt(sinalpha//2))) are orthogonal and vector vec a=(1,3,sin2alpha) makes an obtuse angle with the z-axis, then the value of alpha is a alpha=tan^(-1)2 b. alpha=-tan^(-1)2 c. alpha=tan^(-1)2 d. alpha=tan^(-1)2

Which of the following identities, wherever defined, hold(s) good? (a) cotalpha-tanalpha=2cot2alpha (b) tan(45^0+alpha)-tan(45^0-alpha)=2cos e c2alpha (c) tan(45^0+alpha)+tan(45^0-alpha)=2sec2alpha (d) tanalpha+cotalpha=2tan2alpha

Prove that: t a nalpha+2tan2alpha+4tan4alpha+8cot8alpha=cotalpha

If cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x , then sinx is tan^2alpha/2 (b) cot^2alpha/2 (c) tan^2alpha (d) cotalpha/2

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