Express the ratios $\cos A ,$ tan $A$ and $\sec A$ in terms of $\sin A .$
Express the ratios $\cos A ,$ tan $A$ and $\sec A$ in terms of $\sin A .$
Since,$\cos ^{2} A+\sin ^{2} A=1,$ therefore
$\cos ^{2} A =1-\sin ^{2} A , i . e ., \cos A =\pm \sqrt{1-\sin ^{2} A }$
This gives $\quad \cos A =\sqrt{1-\sin ^{2} A }$
Hence, $\quad \tan A =\frac{\sin A }{\cos A }=\frac{\sin A }{\sqrt{1-\sin ^{2} A }}$
and $\sec A =\frac{1}{\cos A }=\frac{1}{\sqrt{1-\sin ^{2} A }}$
Similar Questions
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 $\sec$ $A$.
Given $\sec \theta=\frac{13}{12},$ calculate all other trigonometric ratios.
Given $\sec \theta=\frac{13}{12},$ calculate all other trigonometric ratios.
Evaluate:
$\sin 25^{\circ} \cos 65^{\circ}+\cos 25^{\circ} \sin 65^{\circ}$
Evaluate:
$\sin 25^{\circ} \cos 65^{\circ}+\cos 25^{\circ} \sin 65^{\circ}$
State whether the following are true or false. Justify your answer.
$\sin \theta=\cos \theta$ for all values of $\theta$
State whether the following are true or false. Justify your answer.
$\sin \theta=\cos \theta$ for all values of $\theta$
Evaluate:
$\cos 48^{\circ}-\sin 42^{\circ}$
Evaluate:
$\cos 48^{\circ}-\sin 42^{\circ}$