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

Prove that, costhetacos((theta)/(2))-cos3thetacos((9theta)/(2))=sin7thetasin8theta .

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

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

If sintheta+sin^2theta=1, then prove that cos^(12)theta+3cos^10theta+3cos^8theta+cos^6theta+2cos^4theta+2cos^2theta-2=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 ]

Prove that, (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)

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

By using above basic addition/ subtraction formulae, prove that (i) tan (A+B)=(tan A+tan B)/(1-tan A tan B) , (ii) tan (A-B)=(tan A-tanB)/(1+tan A tan B) (iii) sin2theta=2sintheta costheta , (iv) cos2theta=cos^(2)theta=1-2sin^(2)theta=2cos^(2)theta-1 (v) tan 2theta=(2 tan theta)/(1-tan^(2) 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: (sec8theta-1)/(sec4theta-1)=(tan8theta)/(tan2theta)