Prove : `(sin A + cosec A)^2 + (cosA + secA )^2=7 + (tan^2 A+ cot^2 A)`

Prove that (sin^2A)/(cosA) + cos A = sec A.

Prove that: (xi) cosec^2 A - cos^2 A = (sec^2 A - sin^2 A)/(tan^2 A)

cosec A- 2cot 2A cos A=

sin A=1/2, cosA=?

Prove that: (xiii) (cos^2 A + tan^2 A -1)/ (sin^2 A) = tan^2 A

Prove that : (sin theta)/(1 - costheta) = cosec theta + cot theta

If sin A=a cos B and cosA=b sinB then, (a^2 - 1) tan^2 A+(1 -b^2)tan^2B is equal to

Prove that (tan A)/(sec A -1) + (tan A)/(sec A +1) = 2 cosec A

Prove that : (1-sin theta cos theta)/ (cos theta (sec theta - cosec theta)) times (sin^2 theta - cos^2 theta)/(sin^3 theta + cos^3 theta) = sin theta

Prove the following: cosecA-2cot2A.cosA=2sinA