Evaluate: `("lim")_(thetavec0)(cos^2(1-cos^2(1-cos^2(1-cos^2(theta)))))/ (sin(pi(sqrt((theta+4))-2)/theta))`

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

(1)/(sin^(2)theta)-(cos^(2)theta)/(sin^(2) theta) =___.

Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

Range of f(theta)=cos^2theta(cos^2theta+1)+2sin^2theta is

Prove: sin^(8)theta-cos^(8)theta=(sin^(2)theta-cos^(2)theta)(1-2sin^(2)thetacos^(2)theta)

Evaluate underset(theta rarr 0)(lim) (1- cos m theta)/(1- cos n theta)

Given cot theta =(7)/(8) , then evaluate (i) ((1+sin theta )( 1-sin theta ))/( (1+cos theta )(1-cos theta )) " "(ii) ((1+sin theta ))/( cos theta )

Let f_n(theta)=(cos(theta/2)+cos2theta+cos((7theta)/2)+....+cos(3n-2)(theta/2))/(sin(theta/2)+sin2theta+sin((7theta)/2)+....+sin(3n-2)(theta/2)) then (a) f_3((3pi)/(16))=sqrt(2)-1 (b) f_5(pi/(28))=sqrt(2)+1 (c) f_7(pi/(60))=(2+sqrt(3)) (d) none of these

Prove that: (sin2theta)/(1-cos2theta)=cottheta

Evaluate: int_0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2theta d theta dot