(C) Given $A = \frac{5\pi}{4}$.We need to find the value of $\cos A - \sin A$.$\cos\left(\frac{5\pi}{4}\right) - \sin\left(\frac{5\pi}{4}\right) = \co

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) Given $A = \frac{5\pi}{4}$.We need to find the value of $\cos A - \sin A$.$\cos\left(\frac{5\pi}{4}\right) - \sin\left(\frac{5\pi}{4}\right) = \cos\left(\pi + \frac{\pi}{4}\right) - \sin\left(\pi + \frac{\pi}{4}\right)$.Since $\cos(\pi + \theta) = -\cos \theta$ and $\sin(\pi + \theta) = -\sin \theta$,we have:$= -\cos\left(\frac{\pi}{4}\right) - (-\sin\left(\frac{\pi}{4}\right))$$= -\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = 0$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

Easy

The value of $\cos A - \sin A$ when $A = \frac{5\pi}{4}$ is

A
$\sqrt{2}$
B
$\frac{1}{\sqrt{2}}$
C
$0$
D
$1$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Ratios, Functions and Identities

Subtopic

Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

$A$ circular wire of diameter $10 \, cm$ is cut and placed along the circumference of a circle of diameter $1 \, m$. The angle subtended by the wire at the centre of the circle is equal to:

Easy

View Solution

If $\tan \theta = -\frac{4}{3},$ then $\sin \theta = $

MediumIIT 1979

View Solution

In a right-angled triangle $ABC$ where $\angle C = 90^{\circ}$,$AC = BC$. If $D$ is the midpoint of $AC$,then the cotangent of $\angle DBC$ is equal to:

Easy

View Solution

$\cot (45^\circ + \theta ) \cot (45^\circ - \theta ) = $

Easy

View Solution

If $\theta$ lies in the third quadrant and $\cos \theta = -\frac{3}{5}$,find the value of $\tan \theta$.

EasyAP EAMCET 2020

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

The value of $\cos A - \sin A$ when $A = \frac{5\pi}{4}$ is

Similar Questions

$A$ circular wire of diameter $10 \, cm$ is cut and placed along the circumference of a circle of diameter $1 \, m$. The angle subtended by the wire at the centre of the circle is equal to:

If $\tan \theta = -\frac{4}{3},$ then $\sin \theta = $

In a right-angled triangle $ABC$ where $\angle C = 90^{\circ}$,$AC = BC$. If $D$ is the midpoint of $AC$,then the cotangent of $\angle DBC$ is equal to:

$\cot (45^\circ + \theta ) \cot (45^\circ - \theta ) = $

If $\theta$ lies in the third quadrant and $\cos \theta = -\frac{3}{5}$,find the value of $\tan \theta$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module