Question

prove that sin square 1 degree + sin square 3 degree + sin square5 degree + ......... + sin square 89 = 22.5

Answer 1

there comes the answer

Answer 2

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

Step-by-step explanation:

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.