Write all the other trigonometric ratios of $\angle A$ in terms of $\sec$ $A$.
Write all the other trigonometric ratios of $\angle A$ in terms of $\sec$ $A$.
We know that,
$\cos A=\frac{1}{\sec A}$
Also, $\sin ^{2} A+\cos ^{2} A=1$
$\sin ^{2} A=1-\cos ^{2} A$
$\sin A=\sqrt{1-\left(\frac{1}{\sec A}\right)^{2}}$
$=\sqrt{\frac{\sec ^{2} A-1}{\sec ^{2} A}}=\frac{\sqrt{\sec ^{2} A-1}}{\sec A}$
$\tan ^{2} A+1=\sec ^{2} A$
$\tan ^{2} A=\sec ^{2} A-1$
$\tan A =\sqrt{\sec ^{2} A -1}$
$\cot A =\frac{\cos A }{\sin A } =\frac{\frac{1}{\sec A}}{\frac{\sqrt{\sec ^{2} A-1}}{\sec A}}$
$=\frac{1}{\sqrt{\sec ^{2} A-1}}$
$\operatorname{cosec} A =\frac{1}{\sin A }=\frac{\sec A }{\sqrt{\sec ^{2} A -1}}$
Similar Questions
Given $\tan A=\frac{4}{3},$ find the other trigonometric ratios of the $\angle A$
Given $\tan A=\frac{4}{3},$ find the other trigonometric ratios of the $\angle A$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\frac{1+\sec A}{\sec A}=\frac{\sin ^{2} A}{1-\cos A}$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\frac{1+\sec A}{\sec A}=\frac{\sin ^{2} A}{1-\cos A}$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\frac{\sin \theta-2 \sin ^{3} \theta}{2 \cos ^{3} \theta-\cos \theta}=\tan \theta$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\frac{\sin \theta-2 \sin ^{3} \theta}{2 \cos ^{3} \theta-\cos \theta}=\tan \theta$
If $\sin A =\frac{3}{4},$ calculate $\cos A$ and $\tan A$.
If $\sin A =\frac{3}{4},$ calculate $\cos A$ and $\tan A$.
Evaluate:
$\cos 48^{\circ}-\sin 42^{\circ}$
Evaluate:
$\cos 48^{\circ}-\sin 42^{\circ}$