InterviewSolution
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InterviewSolution
| 1. |
( sin theta + cos theta ) ( tan theta + cot theta ) = sec theta + csc theta prove it |
| Answer» L.H.S.\xa0{tex}= (\\sin \\theta + \\cos \\theta )(\\tan \\theta + \\cot \\theta ){/tex}{tex}= (\\sin \\theta + \\cos \\theta )\\left( {\\frac{{\\sin \\theta }}{{\\cos \\theta }} + \\frac{{\\cos \\theta }}{{\\sin \\theta }}} \\right){/tex}{tex}= (\\sin \\theta + \\cos \\theta )\\left( {\\frac{{{{\\sin }^2}\\theta + {{\\cos }^2}\\theta }}{{\\sin \\theta \\cos \\theta }}} \\right){/tex}{tex} = (\\sin \\theta + \\cos \\theta )\\left( {\\frac{1}{{\\sin \\theta \\cos \\theta }}} \\right){/tex}{tex} = \\frac{{\\sin \\theta + \\cos \\theta }}{{\\sin \\theta \\cos \\theta }}{/tex}{tex} = \\frac{{\\sin \\theta }}{{\\sin \\theta \\cos \\theta }} + \\frac{{\\cos \\theta }}{{\\sin \\theta \\cos \\theta }}{/tex}{tex}= \\frac{1}{{\\cos \\theta }} + \\frac{1}{{\\sin \\theta }}{/tex}{tex}= \\sec \\theta + \\cos ec\\theta {/tex}= R.H.S. | |