`"If "f(theta)=tan (sin^(-1)sqrt((2)/(3+cos 2theta)))," then "`

If f(theta)=tan(sin^(-1)sqrt((2)/(3+cos2 theta))) ,then: (A) f^(')((pi)/(4))=sqrt(2) (B) f((pi)/(4))=sqrt(2) (C) (d(f(theta)))/(d(cos theta)) at theta=(pi)/(4) is -sqrt(2) (D) (d(f(theta)))/(d(cos theta)) at theta=(pi)/(4) is -2

If f(theta)=sin(tan^(-1)((sin theta)/(sqrt(cos2 theta)))), where -(pi)/(4)

If u=tan^(-1)(1/(sqrt(cos 2 theta)))-tan^(-1)(sqrt(cos 2 theta)) , then sin u=

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

If u= cot ^(-1) (sqrt(cos 2 theta)) -tan ^(-1)(sqrt(cos 2 theta)) , then prove that : sin u = tan^(2) theta .

If f(theta) = sin(tan^(-1)(("sin theta)/(sqrt(cos 2 theta)))) , where -pi/4 lt theta lt pi/4 , then the value of d/(d(tan theta)) f(theta) is

Let f(theta)=sin(tan^(-1)((sin theta)/(sqrt(cos2 theta)))), wher e-(pi)/(4)

If u = cot^(-1) sqrt(cos 2theta) - tan^(-1) sqrt(cos 2theta) prove that sin u = tan^(2) theta . .

The range of f(theta)=3cos^2theta-8sqrt(3) cos theta sin theta + 5 sin^2theta-7 is gven by