Question

prove that sin square A.cot square A+cos square A.tan square A=1

Answer 1

sin^2A.cot^2A+cos^2A.tan^2A
=sin^2A.cos^2A/sin^2A+cos^2A.sin^2A/cos^2A
=cos^2A+sin^2A
=1=R•H•S•

Answer 2

Consider the provided information.

\sin^2A\cos^2B-\cos^2A\sin^2B=\sin^2A-\sin^2B

Consider the LHS.

\sin^2A\cos^2B-\cos^2A\sin^2B

\sin^2A(1-\sin^2B)-(1-\sin^2A)\sin^2B               (∴\cos^2x=1-\sin^2x)

\sin^2A-\sin^2A\sin^2B-\sin^2B+\sin^2A\sin^2B

\sin^2A-\sin^2B

Hence, proved.