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

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

If cot(sin^(-1)sqrt(1-x^2))=sin(tan^(-1)(xsqrt(6))),\ x!=0 , then possible value of x is

Show that (1- tan ^(2) A ) /( cot ^(2) A-1) =tan ^(2) A

If 3 sin alpha=5 sin beta , then (tan((alpha+beta)/2))/(tan ((alpha-beta)/2))=

If costheta=(cosalphacosbeta)/(1-sinalphasinbeta) then prove that tan((theta)/(2))=(tan((alpha)/(2))-tan((beta)/(2)))/(1-tan((alpha)/(2))tan((beta)/(2)))

If Delta_(1) is the area of the triangle with vertices (0, 0), (a tan alpha, b cot alpha), (a sin alpha, b cos alpha), Delta_(2) is the area of the triangle with vertices (a sec^(2) alpha, b cos ec^(2) alpha), (a + a sin^(2)alpha, b + b cos^(2)alpha) and Delta_(3) is the area of the triangle with vertices (0,0), (a tan alpha, -b cot alpha), (a sin alpha, b cos alpha) . Show that there is no value of alpha for which Delta_(1), Delta_(2) and Delta_(3) are in GP.

If msintheta=nsin(theta+2alpha) , then prove that tan(theta+alpha)cotalpha=(m+n)/(m-n) .

If alpha+beta+gamma=2pi , then show that tan.alpha/2 + tan.beta/2 + tan.gamma/2 = tan.alpha/2 tan.beta/2 tan.gamma/2 .

If cos^(-1)x/a+cos^(-1)y/b=alpha, prove that (x^2)/(a^2)-2(x y)/(a b)cosalpha+(y^2)/(b^2)=sin^2alpha