Express ` 1/(1 + cos theta - I sin theta ) ` in the form of a +ib .
Hint : ` sin^(2)theta+ cos^(2) theta=1`

cos^2theta (1+sin^(2) theta )=1

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

If sin theta = cos theta find the value of : 3 tan ^(2) theta+ 2 sin ^(2) theta -1

Prove that (1 - cos 2 theta)/( sin 2 theta) = tan theta.

If cos theta + sin theta =sqrt(2) cos theta prove that cos theta -sin theta =sqrt(2) sin theta

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

sin^(3)theta + sin theta - sin theta cos^(2)theta =

Express 2cos theta + 3 sin theta in the form r cos ( theta - alpha ), where r is positive, stating the values of r and alpha. What is the maximum value of 2 cos theta + 3 sin theta ?

The roots of the equation |(3x^(2),x^(2) + x cos theta + cos^(2) theta ,x^(2) + x sin theta + sin^(2) theta),(x^(2) + x cos theta + cos^(2) theta,3 cos^(2) theta,1 + (sin 2 theta)/(2)),(x^(2) + x sin theta + sin^(2) theta,1 + (sin 2 theta)/(2),3 sin^(2) theta)| = 0

cos theta + sin theta - sin 2 theta = (1)/(2), 0 lt theta lt (pi)/(2)