(B) Given $0 < \theta < \frac{\pi}{2}$ and $\sin \theta \cos \theta = \frac{12}{25}$.We need to find $\sin^4 \theta + \cos^4 \theta$.Using the identit

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

(B) Given $0 We need to find $\sin^4 \theta + \cos^4 \theta$.Using the identity $a^2 + b^2 = (a + b)^2 - 2ab$,we have:$\sin^4 \theta + \cos^4 \theta = (\sin^2 \theta)^2 + (\cos^2 \theta)^2$$= (\sin^2 \theta + \cos^2 \theta)^2 - 2 \sin^2 \theta \cos^2 \theta$Since $\sin^2 \theta + \cos^2 \theta = 1$,we get:$= (1)^2 - 2(\sin \theta \cos \theta)^2$$= 1 - 2 \left(\frac{12}{25}\right)^2$$= 1 - 2 \left(\frac{144}{625}\right)$$= 1 - \frac{288}{625}$$= \frac{625 - 288}{625} = \frac{337}{625}$.

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

Medium

If $0 < \theta < \frac{\pi}{2}$ and $\sin \theta \cos \theta = \frac{12}{25}$,then $\sin^4 \theta + \cos^4 \theta$ is equal to

AP EAMCET 2021 All AP EAMCET

A
$\frac{327}{625}$
B
$\frac{337}{625}$
C
$\frac{347}{625}$
D
$\frac{340}{625}$

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

Previous Year

AP EAMCET 2021 Paper All AP EAMCET years →

If the roots of $x^3 + ax^2 + bx + c = 0$ are the cosines of the angles of an acute triangle,then the value of $a^2 - 2b - 2c$ is:

View Solution

If $\cos \alpha + \cos \beta = \frac{3}{2}$ and $\sin \alpha + \sin \beta = \frac{1}{2}$ and $\theta$ is the arithmetic mean of $\alpha$ and $\beta$,then $\sin 2\theta + \cos 2\theta$ is equal to

DifficultJEE MAIN 2015

View Solution

The expression $(1 + \tan x + \tan^2 x)(1 - \cot x + \cot^2 x)$ has positive values for $x$,given by

Easy

View Solution

$\sin 20^{\circ}(4+\sec 20^{\circ})=$

MediumTS EAMCET 2024

View Solution

If $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$ and $\alpha+\beta \neq \frac{\pi}{2}$,then $\frac{\tan \left(\frac{\pi}{4}-\alpha\right)}{\tan \left(\frac{\pi}{4}-\beta\right)}=$

MediumTS EAMCET 2025

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 $0 < \theta < \frac{\pi}{2}$ and $\sin \theta \cos \theta = \frac{12}{25}$,then $\sin^4 \theta + \cos^4 \theta$ is equal to

Similar Questions

If the roots of $x^3 + ax^2 + bx + c = 0$ are the cosines of the angles of an acute triangle,then the value of $a^2 - 2b - 2c$ is:

If $\cos \alpha + \cos \beta = \frac{3}{2}$ and $\sin \alpha + \sin \beta = \frac{1}{2}$ and $\theta$ is the arithmetic mean of $\alpha$ and $\beta$,then $\sin 2\theta + \cos 2\theta$ is equal to

The expression $(1 + \tan x + \tan^2 x)(1 - \cot x + \cot^2 x)$ has positive values for $x$,given by

$\sin 20^{\circ}(4+\sec 20^{\circ})=$

If $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$ and $\alpha+\beta \neq \frac{\pi}{2}$,then $\frac{\tan \left(\frac{\pi}{4}-\alpha\right)}{\tan \left(\frac{\pi}{4}-\beta\right)}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module