If `tan^2theta=2tan^2phi+1` , prove that `cos2theta+sin^2phi=0.`

If 3sin^(2)theta + 2sin^(2)phi = 1 and 3sin 2theta = 2sin 2phi , 0lt0ltpi/2 and 0ltphiltpi/2 , then the value of theta + 2phi is :

If 2 sin^(2) theta +5 cos theta=4 , Prove that cos theta=1//2

If 2 sin^(2) theta +5 cos theta=4 , Prove that cos theta=1//2

If 2 sin^(2) theta +5 cos theta=4 , Prove that cos theta=1//2

If tan theta=(b)/(a) then a cos 2 theta+b sin 2 theta=

If (1 + tan theta) (1+ tan phi) = 2, then theta + phi =

For any acute angle theta , prove that: (i) sin^(2) theta + cos^(2) theta =1

If sin 2 theta+sin 2 phi=(1)/(2) and cos 2 theta+cos 2 phi=(3)/(2) then cos ^(2)(theta-phi)=

Prove that cot^2(90^@-theta)/(tan^2theta-1)+Cosec^2theta/(sec^2theta-cosec^2theta)=1/(sin^2theta-cos^2theta) .

If tan theta = 3/4, cos^(2) theta - sin^(2) theta = _______