Question

Express all the trigonometric ratios in terms of cos a

Answer 1

$\qquad \red{\large \sf \: sin \:A \: = \sqrt{1 - {cos}^{2} \: A} }$

$\qquad\large \green {\sf \: tan \: A \: = \frac{sin \: A}{cos \: A} = \frac{ \sqrt{1 - cos {}^{2} \: A } }{cos \:A } }$

$\: \qquad \large \pink{ \sf \: cosec \:A \: = \frac{1}{sin \: A} = \frac{1}{ \sqrt{1 - {cos}^{2} \:A } } }$

$\large \blue{ \sf \: cot \: A = \frac{1}{tan \: A} = \frac{cos \: A}{1 - {cos}^{2} \: A} }$

$\qquad\large \orange{ \sf \: sec \: A = \frac{1}{cos \:A } }.$

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More information

$\purple{\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\bf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}}$