Prove that : `sec theta + cos theta != 3/2`

Prove that : (cos 4theta + cos 3theta + cos 2theta)/(sin 4theta + sin 3theta + sin 2theta) = cot 3theta

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

Prove that : ( sin theta- cos theta +1)/( sin theta +cos theta -1) = (1)/( sec theta - tan theta)

Prove that ( cos theta + cos 2 theta + cos 3 theta + cos 4 theta)/(sin theta + sin 2 theta + sin 3 theta + sin 4 theta)= cot ""(5theta)/(2).

Prove that : (sec 8theta - 1)/(sec 4theta - 1) = (tan 8theta)/(tan 2theta)

Prove that sec theta + tan theta = tan (pi/4 + theta/2)

Prove that : sin theta cos^3 theta - cos theta sin^3 theta = 1/4 sin4theta .

Prove that : (sin 5theta - 2 sin 3theta + sin theta)/(cos 5theta -cos theta) = tan theta

i) sec(theta) = cos(theta)

Prove that : (sin theta + sec theta) ^(2) + (cos theta + cosec theta) ^(2) = (1 + sec theta cosec theta) ^(2).