" If `theta=sin^(-1)(a^(2)+1)+cos^(-1)(a^(2)+1)-cot^(-1)(a^(2)+1)` then value of `sec^(2)theta` is : "

If tan^(-1)(sin^(2)theta-2sin theta+3)+cot^(-1)(5^(sec^(2)y)+1)=(pi)/(2) then value of cos^(2)theta-sin theta is equal to 0(b)-1(c)1 (d) none of these

Find the value of (sec^(2)theta-1).cot^(2)theta

If 1/(sin^(2)theta)-1/(cos^(2) theta)-1/(tan^(2)theta)-1/(cot^(2)theta)-1/(sec^(2)theta)-1/(cosec^(2)theta)=-3 then find the value of theta .

Prove each of the following identities : (i) (sec^(2) theta -1) cot^(2) theta =1 " " (ii) (sec^(2) theta -1) ("cosec"^(2)theta -1) =1 (iii) (1- cos^(2) theta )sec^(2) theta = tan^(2) theta

The value of sin^(2)theta cos^(2)theta(sec^(2)theta+cosec^(2)theta)-1 is

sin^(4) theta + 2 cos^(2) theta (1 - (1)/( sec^(2) theta)) + cos ^(4) theta =

(tan theta)/((1+tan^(2)theta)^(2))+(cot theta)/((1+cot^(2)theta)^(2))=sin theta cos theta

cos^(2)theta+1/(1+cot^(2)theta)=1

If sin theta+sin phi=(1)/(2) and cos theta+cos phi=1 then find the value of cot((theta+phi)/(2))

Prove that : (tan^(3) theta)/(1+tan^(2)theta) +(cot^(3)theta)/(1+cot^(2)theta) = sec theta "cosec " theta - 2 sin theta cos theta .