Simplify:
( a )  ` Sin^2(theta) + Cos^2( theta )`
( b ) ` Cos^2(theta ) - Sin^2(theta )`

Simplify cos^2theta-sin^2theta

Simplify sqrt(1- sin^2theta ) + (1 cos^2theta)

Simplify: (sin8 theta cos theta-sin6 theta cos3 theta)/(cos2 theta cos theta-sin3 theta sin4 theta)

(cos theta-sin theta) / (cos theta + sin theta) = sec2 theta-tan2 theta

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

2 cos (theta - pi //2) + 3 sin (theta + pi//2) - (3sin theta + 2 cos theta ) = ? A. cos theta - sin theta B. sin theta - cos theta C. sin theta + cos theta D. cot theta - tan theta .

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

If cos theta =4/5 then sin^2 theta cos theta + cos^2 theta sin theta is equal to :

Simplify (sin^(2)theta)/(1+cos theta)+(sin^(2)theta)/(1-cos theta)