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 ) [use the identity sec ^(2) theta =1 +tan ^(2) theta ]

Show that (cosec theta -cot theta )^(2) =(1-cos theta )/( 1+cos theta )

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

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

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

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

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, (2costheta+1)(2costheta-1) (2cos2theta-1)(2cos4theta-1)=2cos8theta+1

Prove : (2 sin theta cos theta-cos theta)/(1-sin theta+sin^(2) theta-cos^(2) theta)=cot theta

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 )