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

Prove that sqrt ((1+cos theta )/( 1-cos theta ) ) = cosec theta +cot theta , 0le theta le 90 ^(@)

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 ]

Let theta in (pi//4,pi//2), then Statement I (cos theta)^(sin theta ) lt ( cos theta )^(cos theta ) lt ( sin theta )^(cos theta ) Statement II The equation e^(sin theta )-e^(-sin theta )=4 ha a unique solution.

Prove that cos theta cos 2theta cos2^2 theta … cos 2^(n-1) theta = (sin2^n theta)/(2^n.sin theta) , for all n in N

If tan((pi)/(2) sin theta )= cot((pi)/(2) cos theta ) , then sin theta + cos theta is equal to

Given cot theta =(7)/(8) , then evaluate (i) ((1+sin theta )( 1-sin theta ))/( (1+cos theta )(1-cos theta )) " "(ii) ((1+sin theta ))/( cos theta )

Show that the normal at any point theta to the curve x = a cos theta + a theta sin theta, y = a sin theta - a theta cos theta is at the constant distance from origin.

For which value of an acute angle theta ,(i) ( cos theta )/( 1-sin theta ) +(cos theta )/( 1+sin theta ) =4 is true ? For which value of 0^(@) le theta le 90 ^(@) , above equation is not defined?

Show that cot theta +tan theta =sec theta cosec theta