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

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 .

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

If sin theta_(1)sin theta_(2)-cos theta_(1)cos theta_(2)+1=0, then the value of tan((theta_(1))/(2))cot((theta_(2))/(2)) is equal to (a) -1( b) 1(c)2(d)-2

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

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

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