Prove the following identity: `(s e c A\ s e c B+t a n AtanB)^2-(s e c A\ t a n B+t a n A s e c B)^2=1`

Prove the following identity: (t a n A)/(1-cot A)+(cot A)/(1-t a n A)=(s e c A\ cos e c\ A+1)

Prove the following identity: (1+cottheta-cos e ctheta)(1+t a ntheta+s e ctheta)=2

Prove the following identity: cos e c\ theta(s e ctheta-1)-cottheta(1-costheta)=t a ntheta-sintheta

Differentiate the following function with respect of x :(xtanx)/(s e c x+t a n x)

Prove the following identity: (t a ntheta+s e ctheta-1)/(t a ntheta-s e ctheta+1)=(1+sintheta)/(costheta)

If A+B+C=180^0 , then (t a n A+t a n B+t a n C)/(t a n A\ t a n B\ t a n C) is equal to a. t a n A t a n B t a n C b. 0 c. 1 d. none of these

If A , B , C are angles of a triangle which of the following will not imply it is equilateral t a n A+t a n B+t a n C=3sqrt(3) cot A+cot B+"c o t C"=sqrt(3) a+b+c=2R a^2+b^2+c^2=9R^2

If the angles of ∆ABC are in ratio 1:1:2, respectively (the largest angle being angle C), then the value of s e c A c o s e c B secAcosecB - t a n A c o t B tanAcotB is (a) 0 (b) 1/2 (c) 1 (d) √3/2

If A+B+C=pi,\ t h e n\ |"sin"(A+B+C)s in B cos C-s in B0t a n A"cos"(A+B)-t a n A0| is equal to 2s in B t a n A cos C b. 1 c. 0 d. none of these

Consider the following statements : S_(1) : If A={a} and B = {a, b, c}, then A in B . S_(2) : If n(A)=x, then n(P(A))=2^(x) . S_(3) : (AuuB)sube A . S_(4) : phi is subset of every set State, in order, whether S_(1), S_(2), S_(3), S_(4) and true or false (a) T T T T (b) FT T F (c) FTFT (d) FFT T