if` a cos theta + b sin theta = c.` then what is the value of `a sin theta -b cos theta`

If a cos theta-b sin theta = c, then find the value of a sin theta + b cos theta.

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

If tan theta = b/a, then find the value of a cos 2theta + b sin 2theta .

If sin theta_1 + sintheta_2 + sin theta_3 = 3 then find the value of cos theta_1 + cos theta_2 + cos theta_3.

Let sin theta-cos theta=1 then the value of sin^(3) theta-cos^(3)theta is :

Statement I If 2 cos theta + sin theta=1(theta != (pi)/(2)) then the value of 7 cos theta + 6 sin theta is 2. Statement II If cos 2theta-sin theta=1/2, 0 lt theta lt pi/2 , then sin theta+cos 6 theta = 0 .

If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos theta sin theta , sin^(2) theta , cos theta ],[sin theta ,-cos theta , 0]] ,then f ( pi / 7) is

If 5 cos theta = 6 , sin theta , evalutate : (12 sin theta - 3cos theta)/(12 sin theta + 3 cos theta)

If sin(pi cos theta) = cos(pi sin theta) , then the value of cos(theta+- pi/4) is

If x sin^3 theta+ y cos^3 theta = sin theta cos theta and x sin theta = y cos theta, Find the value of x^2 + y^2.