If `costheta + sin theta = sqrt2 cos theta`, prove that `cos theta - sin theta = sqrt2 sin theta`.

If sin theta-sqrt(6)costheta=sqrt(7)costheta. Prove that cos theta+sqrt6 sin theta-sqrt7 sin theta=0.

If sintheta + sin^(2)theta = 1 , prove that cos^(2)theta + cos^(4)theta = 1

Show that (1)/( cos theta ) -cos theta =tan theta .sin theta

Equation of the line passing through the point ( a cos^(3) theta , a sin^(3) theta ) and perpendicular to the line x sec theta + y cosec theta = a is x cos theta - y sin theta = cos 2 theta .

The value of theta , lying between theta =0 and theta=(pi)/(2) and satisfying the equation . |{:(1+ cos^(2 ) theta , sin^(2) theta , 4 sin 4 theta ),(cos^(2) theta , 1+sin^2 theta , 4 sin 4 theta ),(cos^(2) theta , sin^(2) theta , 1+ 4 sin 4 theta ):}|=0 , is

Show that the normal at any point theta to the curve x = a cos theta + a theta sin theta, y = a sin theta - a theta cos theta is at the constant distance from origin.

Let theta in (pi//4,pi//2), then Statement I (cos theta)^(sin theta ) lt ( cos theta )^(cos theta ) lt ( sin theta )^(cos theta ) Statement II The equation e^(sin theta )-e^(-sin theta )=4 ha a unique solution.

If 3 sin theta + 4 cos theta=5 , then find the value of 4 sin theta-3 cos theta .

If cos theta + sin theta = p and sec theta + cosec theta = q , prove that q (p^(2) - 1) = 2p .

Simply (sin75^(@)-sin15^(@))/(cos75^(@)+cos15^(@)) Prove that (a) (sin3A+sinA)SinA+(Cos3A-cosA)cosA=0 (c) (sin8thetacostheta-sin6 thetacos 3 theta)/(cos 2 theta cos theta-sin 3 thetasin4 theta)=tan 2 theta