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| 1. |
(cosA/1-tanA) +(sinA/1-cotA) = cosA+sinA |
| Answer» {tex}\\eqalign{ & = {{\\cos \\,A} \\over {1 - {{\\sin \\,A} \\over {\\cos \\,A}}}} + {{\\sin \\,A} \\over {1 - {{\\cos \\,A} \\over {\\sin \\,A}}}} \\cr & = {{{{\\cos }^2}A} \\over {\\cos A - \\sin A}} + {{{{\\sin }^2}A} \\over {\\sin A - \\cos A}} \\cr & = {{{{\\cos }^2}A - {{\\sin }^2}A} \\over {\\cos A - \\sin A}} \\cr & = {{(\\cos A - \\sin A)(\\cos A + \\sin A)} \\over {\\cos A - \\sin A}} \\cr & = \\sin A + \\cos A \\cr} {/tex} | |