Show that `(1)/( cos theta ) -cos theta =tan theta .sin theta `

(sin theta+cos theta)(tan theta+cot theta)=

If x = theta cos theta + sin theta, y = cos theta- theta sin theta , then dy/dx at theta = pi/2

Prove that (cot theta -cos theta )/( cot theta +cos theta ) =(cos ec theta -1)/( cosec theta +1)

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

Prove that (sin theta -cos theta+1 )/( sin theta + cos theta -1) =(1)/( sec theta -tan theta ) [use the identity sec ^(2) theta =1 +tan ^(2) theta ]

Evaluate the following determinants: (b) |(cos theta, -sin theta),(sin theta, cos theta)| = cos theta (cos theta) - sin theta(-sin theta) = cos^(2) theta + sin^(2) theta = 1

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

Let P={theta : sin theta -cos theta =sqrt2cos theta} and Q={theta : sin theta +cos theta =sqrt2 sin theta} be two sets . Then :

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

(1+cos 2 theta)/(sin 2 theta)=cot theta