prove that cos A /1-tan A +sin square A /sin A-cos A = sin A+ cos A
Answers
Answered by
9
Step-by-step explanation:
LHS
cosA/1-tanA+sin²A/sinA-cosA
=cos²A/cosA-sinA+sin²A/sinA-cosA
=cos²A/cosA-sinA-sin²A/cosA-sinA
=cos²A-sin²A/cosA-sinA
=(cosA-sinA)(cosA+sinA)/cosA-sinA
=sinA+cosA
RHS
Answered by
4
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.
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