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InterviewSolution
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If tan theta+1/tan theta=2;show that:tan^theta+¹/tan^theta=2 |
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Answer» We have,{tex} \\tan \\theta + \\frac { 1 } { \\tan \\theta } = 2{/tex}Squaring both sides, we get{tex}\\Rightarrow \\left( \\tan \\theta + \\frac { 1 } { \\tan \\theta } \\right) ^ { 2 } = 2 ^ { 2 }{/tex}{tex}\\Rightarrow\\quad\\tan^2\\theta+\\frac1{\\tan^2\\theta}+2\\times\\tan\\theta\\times\\frac1{\\tan\\theta}=4{/tex}{tex}\\Rightarrow \\quad \\tan ^ { 2 } \\theta + \\frac { 1 } { \\tan ^ { 2 } \\theta } + 2 = 4{/tex}{tex}\\Rightarrow \\quad \\tan ^ { 2 } \\theta + \\frac { 1 } { \\tan ^ { 2 } \\theta } = 2{/tex}Alternate method, We have{tex}\\tan \\theta + \\frac { 1 } { \\tan \\theta } = 2{/tex}{tex}\\Rightarrow \\quad \\tan ^ { 2 } \\theta + 1 = 2 \\tan \\theta{/tex}{tex}\\Rightarrow \\quad \\tan ^ { 2 } \\theta - 2 \\tan \\theta + 1 = 0{/tex}{tex}\\Rightarrow \\quad ( \\tan \\theta - 1 ) ^ { 2 } = 0{/tex}{tex}\\Rightarrow \\quad \\tan \\theta = 1{/tex}{tex}\\therefore \\quad \\tan ^ { 2 } \\theta + \\frac { 1 } { \\tan ^ { 2 } \\theta } = 1 + 1 = 2{/tex} Thank? |
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