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| 1. |
If sin theta +cos theta =under root2 cos (90°-theta) . determine cot theta. |
| Answer» We have{tex}\\sin \\theta + \\cos \\theta = \\sqrt 2 \\cos (90^\\circ - \\theta ){/tex}{tex} \\Rightarrow \\sin \\theta + \\cos \\theta = \\sqrt 2 \\sin \\theta {/tex}\xa0{tex}\\left[ {\\because \\cos (90^\\circ - \\theta ) = \\sin \\theta } \\right]{/tex}{tex} \\Rightarrow \\cos \\theta = \\sqrt 2 \\sin \\theta - \\sin \\theta {/tex}{tex} \\Rightarrow \\cos \\theta = \\sin \\theta \\left( {\\sqrt 2 - 1} \\right){/tex}{tex} \\Rightarrow \\frac{{\\cos \\theta }}{{\\sin \\theta }} = \\sqrt 2 - 1{/tex}{tex} \\Rightarrow \\cot \\theta = \\sqrt 2 - 1{/tex}\xa0{tex}\\left[ {\\because \\frac{{\\cos \\theta }}{{\\sin \\theta }} = \\cot \\theta } \\right]{/tex} | |