If `phi=cot^(-1)sqrt(cos2theta)-tan^(-1)sqrt(cos2theta)`, then show that, `sin phi=tan^(2)theta`.

If phi="tan"^(-1)(xsqrt(3))/(2k-x) and theta="tan"^(-1)(2x-k)/(k sqrt(3)) , then show that one value of (phi-theta) is 30^(@) .

If cos theta+sin theta = sqrt2 cos theta , then show cos theta-sin theta = sqrt2 sin theta .

tan ( 2 tan ^(-1)sqrt((1+cos theta)/(1-cos theta)))+ tan theta =0

If cos^2theta-sin^2 theta = tan^2 alpha , then show that cos^2 alpha -sin^2 alpha = tan^2 theta .

If sin^4theta+sin^2 theta=1 show that, tan^4theta-tan^2theta=1 .

If cos theta-sin theta=sqrt(2)cos theta , then prove that cos theta+sin theta=pm sqrt(2) sin theta .

(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?

cos2theta = (sqrt(2)+1)(costheta -1/sqrt(2))

If cos theta - sin theta = sqrt2 sin theta , then show that cos theta+sin theta = sqrt2 cos theta .

If phi = tan^-1 (xsqrt3)/(2k-x) and theta (2x-k)/(ksqrt3) , then show that one value of (phi - theta) is 30^@