Express the ratios $\cos A$,$\tan A$,and $\sec A$ in terms of $\sin A$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) We know the fundamental trigonometric identity: $\cos^2 A + \sin^2 A = 1$.
$1$. To express $\cos A$ in terms of $\sin A$:
$\cos^2 A = 1 - \sin^2 A$
$\cos A = \sqrt{1 - \sin^2 A}$ (taking the positive root for acute angle $A$)
$2$. To express $\tan A$ in terms of $\sin A$:
$\tan A = \frac{\sin A}{\cos A}$
Substituting the value of $\cos A$:
$\tan A = \frac{\sin A}{\sqrt{1 - \sin^2 A}}$
$3$. To express $\sec A$ in terms of $\sin A$:
$\sec A = \frac{1}{\cos A}$
Substituting the value of $\cos A$:
$\sec A = \frac{1}{\sqrt{1 - \sin^2 A}}$

Explore More

Similar Questions

Prove the following identity,where the angles involved are acute angles for which the expressions are defined:
$\frac{\cos A-\sin A+1}{\cos A+\sin A-1}=\operatorname{cosec} A+\cot A$,using the identity $\operatorname{cosec}^{2} A=1+\cot ^{2} A$.

Difficult
View Solution

State whether the following is true or false. Justify your answer.
$\cot A$ is not defined for $A = 0^{\circ}$.

Prove the following identity,where the angles involved are acute angles for which the expressions are defined:
$\frac{\tan \theta}{1-\cot \theta}+\frac{\cot \theta}{1-\tan \theta}=1+\sec \theta \operatorname{cosec} \theta$

Difficult
View Solution

Evaluate the following:
$\frac{\cos 45^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}}$

Difficult
View Solution

Evaluate:
$\frac{\tan 26^{\circ}}{\cot 64^{\circ}}$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo