Let `f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta)))),w h e r e-pi/4

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

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

Let f(theta)=sintheta(sintheta+sin3theta).Then, f(theta)

Comprehension 1 Let a^((log)_b x)=c w h e r e a , b , c & x are parameters. On the basis of above information, answer the following questions: If a=b=2xx3^sin^2theta+1/(1+tan^(2theta)) & c=(4 t a ntheta)/(sqrt(sec^2theta-1))(w h e r e theta lies in Ist Quadrant) , then x is- a.3 b. -3 c. 0 d. 4

The value of the expression ((sin3theta)/(sintheta))^2-((cos3theta)/(costheta))^2,w h e ntheta=(7. 5)^0, is a. 4(sqrt(3)+1) b. (sqrt(3)-1) c. 2(sqrt(6)+sqrt(2)) d. 8/(sqrt(6)-sqrt(2))

If f(x) is continuous at theta= pi/4 , where f(theta)={:{((1-tan theta)/(1-sqrt(2)sin theta) ", for " theta!=pi/4),(k/2 ", for " theta=pi/4):} , then k=

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

(sintheta+sin2theta)/(1+costheta+cos2theta) =