Express $\sin 67^{\circ} + \cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) To express the given expression in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$,we use the complementary angle identities:
$\sin(90^{\circ} - \theta) = \cos \theta$
$\cos(90^{\circ} - \theta) = \sin \theta$
Given expression: $\sin 67^{\circ} + \cos 75^{\circ}$
Step $1$: Rewrite $67^{\circ}$ as $(90^{\circ} - 23^{\circ})$ and $75^{\circ}$ as $(90^{\circ} - 15^{\circ})$.
$= \sin(90^{\circ} - 23^{\circ}) + \cos(90^{\circ} - 15^{\circ})$
Step $2$: Apply the complementary angle identities.
$= \cos 23^{\circ} + \sin 15^{\circ}$
Since $23^{\circ}$ and $15^{\circ}$ are both between $0^{\circ}$ and $45^{\circ}$,the expression is now in the required form.

Explore More

Similar Questions

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

Difficult
View Solution

Prove that $\frac{\sin \theta-\cos \theta+1}{\sin \theta+\cos \theta-1}=\frac{1}{\sec \theta-\tan \theta},$ using the identity $\sec ^{2} \theta=1+\tan ^{2} \theta.$

Difficult
View Solution

Given $\tan A = \frac{4}{3},$ find the other trigonometric ratios of the $\angle A$.

In a right triangle $ABC$,right-angled at $B$. If $\tan A = 1$,then verify that $2 \sin A \cos A = 1$.

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

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