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Express the cosA in terms of …

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Express the cosA in terms of cotA

Posted by Kishan Upadhyay 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

tan A = {tex}=\frac{1}{\cot A}{/tex}
{tex}\Rightarrow{/tex} tan² A = {tex}\frac{1}{\cot ^{2} A}{/tex}
{tex}\Rightarrow{/tex} sec² A - 1 = {tex}\frac{1}{\cot ^{2} A}{/tex}
{tex}\Rightarrow{/tex} sec² A = {tex}\frac{1}{\cot ^{2} A}{/tex}+ 1
{tex}\Rightarrow{/tex} sec²A = {tex}\frac{1+\cot ^{2} A}{\cot ^{2} A}{/tex}
{tex}\Rightarrow{/tex} sec A = {tex}\sqrt{\frac{1+\cot ^{2} A}{\cot ^{2} A}}{/tex}
{tex}\Rightarrow{/tex} {tex}\frac{1}{\cos A}=\sqrt{\frac{1+\cot ^{2} A}{\cot ^{2} A}}{/tex}
{tex}\Rightarrow{/tex} cos A = {tex}\sqrt{\frac{\cot ^{2} A}{1+\cot ^{2} A}}{/tex} {tex}=\frac{\cot A}{\sqrt{1+\cot ^{2} A}}{/tex}
{tex}\therefore{/tex} cos A = {tex}\frac{\cot A}{\sqrt{1+\cot ^{2} A}}{/tex}

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