Find r :

`1/r^2 = Cos^2( theta ) /a^2 + Sin^2( theta ) /b^2`

if sin^2theta=1/2 ,then find cos^2theta .

int_ (0) ^ ((pi) / (2)) sin theta cos theta (a ^ (2) sin ^ (2) theta + b ^ (2) cos ^ (2) theta) ^ ((1) / ( 2)) d theta = ((1) / (3)) ((a ^ (2) + ab + b ^ (2)) / (a + b))

Prove each of the following identities : (sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = (2) /((sin^(2) theta - cos^(2) theta)) = (2) /((2sin^(2) theta -1))

If (a^2 -b^2) sin theta + 1ab cos theta = a^2 +b^2 , then find tan theta .

If theta in [0,3 pi] and r in R . Then , find the pair of ( r , theta ) satisfying 2 sin theta = r^(4)- 2r^(2)+3 .

If 2sin theta=2-cos theta find sin theta

Evaluate 2(cos^2theta-sin^2theta)=1

Find the value of (sin^4theta+cos^4theta)/(1-2sin^2 thetacos ^2 theta)

If cos^(2)theta-sin^(2)theta=tan^(2)alpha, "then" : sqrt2 * cos theta * cos alpha=.... A) sin theta * sin alpha B)1 C) tan^(2)theta D)none of these