Evaluate the following and justify your answer.
(i) ` (sin ^(2) 15^(@) +sin ^(2) 75^(@) )/( cos ^(2) 36^(@) +cos ^(2) 54^(@)) `

cos^(2) 45^(@) - sin^(2) 15^(@)=

( sin 75^(@) - sin 15^(@))/( cos 15^(@) - cos 75^(@))=

(sin^(2)3A)/(sin^(2)A)-(cos^(2) 3A)/(cos^(2)A)=

2 cos 54^(@) * sin 66^(@) =

Show that sin^(2) 75^(@) - sin^(2) 15^(@) = (sqrt(3))/(2)

Evaluate the following integrals (i) int_(0)^(pi/2) (sin^(2) x - cos^(2) x)/(sin^(3) x + cos^(3) x) dx

Find the value of cos^(2)72^(@) - sin^(2) 54^(@) .

Evaluate the following: sqrt 2. Sin 45^@ + Cos 90^@ + Sin 90^@

Evaluate the following : (sin theta + cos theta)^(2) + (sin theta - cos theta)^(2)

Find the extreme values of the following function over R. (i) sin^(2) (60^(0) + x) + sin^(2) (60^(0) - x) (ii) cos (x+ (Pi)/(3) ) + 2sqrt(2) sin (x+ (pi)/(3))-3 (iii) 3 sin^(2) x+ 5 cos^(2) x (iv) cos 2 x+ cos^(2) x (v ) cos x cos ((2pi)/(3) + x) cos ((2pi)/(3)-x)