Express trignometric ratios sin A,secA and …
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Posted by Sagar Sagu 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
For sin A,
By using identity {tex}cosec ^ { 2 } A - \cot ^ { 2 } A = 1 \Rightarrow \cos e c ^ { 2 } A = 1 + \cot ^ { 2 } A{/tex}
{tex}\Rightarrow \frac { 1 } { \sin ^ { 2 } A } = 1 + \cot ^ { 2 } A{/tex}
{tex}\Rightarrow \sin A = \frac { 1 } { \sqrt { 1 + \cot ^ { 2 } A } }{/tex}
For secA,
By using identity {tex}\sec ^ { 2 } A - \tan ^ { 2 } A = 1 \Rightarrow \sec ^ { 2 } A = 1 + \tan ^ { 2 } A{/tex}
{tex}\Rightarrow \sec ^ { 2 } A = 1 + \frac { 1 } { \cot ^ { 2 } A } = \frac { \cot ^ { 2 } A + 1 } { \cot ^ { 2 } A } \Rightarrow \sec ^ { 2 } A = \frac { 1 + \cot ^ { 2 } A } { \cot ^ { 2 } A }{/tex}
{tex}\Rightarrow \sec A = \frac { \sqrt { 1 + \cot ^ { 2 } A } } { \cot A }{/tex}
For tanA,
{tex}\tan A = \frac { 1 } { \cot A }{/tex}
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