(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 $\sin x + \sin y = \alpha$ and $\cos x + \cos y = \beta$,then $\operatorname{cosec}(x + y) = $

MediumAP EAMCET 2024

View Solution

The number of ordered pairs $(x, y)$ satisfying the equations $\sin x + \sin y = \sin(x + y)$ and $|x| + |y| = 1$ is

DifficultAP EAMCET 2024

View Solution

If $\cos (\theta - \alpha ), \cos \theta$ and $\cos (\theta + \alpha )$ are in $H.P.$,then $\cos \theta \sec \frac{\alpha }{2}$ is equal to

DifficultIIT 1997

View Solution

The value of $\sum_{k=1}^3 \cos ^2\left((2 k-1) \frac{\pi}{12}\right)$ is equal to

DifficultTS EAMCET 2002

View Solution

If $A$ and $B$ are positive acute angles satisfying $3 \cos^2 A + 2 \cos^2 B = 4$ and $\frac{3 \sin A}{\sin B} = \frac{2 \cos B}{\cos A}$,then $A + 2B =$ (in $^{\circ}$)

DifficultTS EAMCET 2019

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 $\sin x + \sin y = \alpha$ and $\cos x + \cos y = \beta$,then $\operatorname{cosec}(x + y) = $

The number of ordered pairs $(x, y)$ satisfying the equations $\sin x + \sin y = \sin(x + y)$ and $|x| + |y| = 1$ is

If $\cos (\theta - \alpha ), \cos \theta$ and $\cos (\theta + \alpha )$ are in $H.P.$,then $\cos \theta \sec \frac{\alpha }{2}$ is equal to

The value of $\sum_{k=1}^3 \cos ^2\left((2 k-1) \frac{\pi}{12}\right)$ is equal to

If $A$ and $B$ are positive acute angles satisfying $3 \cos^2 A + 2 \cos^2 B = 4$ and $\frac{3 \sin A}{\sin B} = \frac{2 \cos B}{\cos A}$,then $A + 2B =$ (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module