(D) Given $\sin \theta + \text{cosec} \theta = 2$. Since $\text{cosec} \theta = \frac{1}{\sin \theta}$,we have $\sin \theta + \frac{1}{\sin \theta} =

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

(D) Given $\sin \theta + \text{cosec} \theta = 2$. Since $\text{cosec} \theta = \frac{1}{\sin \theta}$,we have $\sin \theta + \frac{1}{\sin \theta} = 2$. Multiplying by $\sin \theta$,we get $\sin^2 \theta + 1 = 2 \sin \theta$. This simplifies to $\sin^2 \theta - 2 \sin \theta + 1 = 0$,which is $(\sin \theta - 1)^2 = 0$. Thus,$\sin \theta = 1$. Therefore,$\sin^{10} \theta + \text{cosec}^{10} \theta = (1)^{10} + \frac{1}{(1)^{10}} = 1 + 1 = 2$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Mix Examples-Trigonometrical Ratios, Functions and Identities

Easy

If $\sin \theta + \text{cosec} \theta = 2$,the value of $\sin^{10} \theta + \text{cosec}^{10} \theta$ is

A
$10$
B
$2^{10}$
C
$2^9$
D
$2$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Ratios, Functions and Identities

Subtopic

Mix Examples-Trigonometrical Ratios, Functions and Identities

If $0 < B < A < \frac{\pi}{4}$,$\cos^2 B - \sin^2 A = \frac{\sqrt{3}+1}{4\sqrt{2}}$ and $2 \cos A \cos B = \frac{1+\sqrt{2}+\sqrt{3}}{2\sqrt{2}}$,then $\cos^2 \frac{4B}{3} - \sin^2 \frac{4A}{5} =$

DifficultTS EAMCET 2024

View Solution

If ${\cos ^6}\alpha + {\sin ^6}\alpha + K{\sin ^2}2\alpha = 1,$ then $K =$

Medium

View Solution

If $\frac{1 - \cos x}{\cos x(1 + \cos x)} = \frac{\sin \alpha}{\cos x} - \frac{2}{1 + \cos x}$,then $\alpha = $

Easy

View Solution

If $\tan (\pi \cos \theta) = \cot (\pi \sin \theta)$,then $\sin \left(\frac{\pi}{4} + \theta\right) =$

MediumMHT CET 2025

View Solution

$1 + \cos 56^\circ + \cos 58^\circ - \cos 66^\circ = $

DifficultIIT 1964

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

If $\sin \theta + \text{cosec} \theta = 2$,the value of $\sin^{10} \theta + \text{cosec}^{10} \theta$ is

Similar Questions

If $0 < B < A < \frac{\pi}{4}$,$\cos^2 B - \sin^2 A = \frac{\sqrt{3}+1}{4\sqrt{2}}$ and $2 \cos A \cos B = \frac{1+\sqrt{2}+\sqrt{3}}{2\sqrt{2}}$,then $\cos^2 \frac{4B}{3} - \sin^2 \frac{4A}{5} =$

If ${\cos ^6}\alpha + {\sin ^6}\alpha + K{\sin ^2}2\alpha = 1,$ then $K =$

If $\frac{1 - \cos x}{\cos x(1 + \cos x)} = \frac{\sin \alpha}{\cos x} - \frac{2}{1 + \cos x}$,then $\alpha = $

If $\tan (\pi \cos \theta) = \cot (\pi \sin \theta)$,then $\sin \left(\frac{\pi}{4} + \theta\right) =$

$1 + \cos 56^\circ + \cos 58^\circ - \cos 66^\circ = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module