(C) Let $f(x) = \sin x + \cos 2x$.Using the identity $\cos 2x = 1 - 2\sin^2 x$,we get:$f(x) = \sin x + 1 - 2\sin^2 x$.Let $t = \sin x$,where $t \in [-

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

(C) Let $f(x) = \sin x + \cos 2x$.Using the identity $\cos 2x = 1 - 2\sin^2 x$,we get:$f(x) = \sin x + 1 - 2\sin^2 x$.Let $t = \sin x$,where $t \in [-1, 1]$.Then $f(t) = -2t^2 + t + 1$.This is a downward-opening parabola. The vertex occurs at $t = -b/(2a) = -1/(2 \times -2) = 1/4$.Since $1/4 \in [-1, 1]$,the maximum value is $f(1/4) = -2(1/4)^2 + (1/4) + 1$.$f(1/4) = -2(1/16) + 1/4 + 1 = -1/8 + 2/8 + 8/8 = 9/8$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

Difficult

What is the maximum value of $f(x) = \sin x + \cos 2x$?

A
$0$
B
$-2$
C
$9/8$
D
None of these

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Ratios, Functions and Identities

Subtopic

Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

The smallest value of $5 \cos \theta + 12$ is

EasyWBJEE 2009

View Solution

The equation $\sin^2 \theta = \frac{x^2 + y^2}{2xy}$,where $x, y \neq 0$,is possible if

Difficult

View Solution

If $\alpha+\beta=\frac{\pi}{2}$ and $\beta+\gamma=\alpha$,then $\tan \alpha$ equals

EasyIIT 2001

View Solution

If $f(x) = \sin^6 x + \cos^6 x$ for $x \in R$,then $f(x)$ lies in the interval

DifficultAP EAMCET 2011

View Solution

Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^2$,where $f(\theta)=\sqrt{a^2 \cos^2 \theta+b^2 \sin^2 \theta} + \sqrt{a^2 \sin^2 \theta+b^2 \cos^2 \theta}$. Then $M-m=$

MediumAP 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

What is the maximum value of $f(x) = \sin x + \cos 2x$?

Similar Questions

The smallest value of $5 \cos \theta + 12$ is

The equation $\sin^2 \theta = \frac{x^2 + y^2}{2xy}$,where $x, y \neq 0$,is possible if

If $\alpha+\beta=\frac{\pi}{2}$ and $\beta+\gamma=\alpha$,then $\tan \alpha$ equals

If $f(x) = \sin^6 x + \cos^6 x$ for $x \in R$,then $f(x)$ lies in the interval

Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^2$,where $f(\theta)=\sqrt{a^2 \cos^2 \theta+b^2 \sin^2 \theta} + \sqrt{a^2 \sin^2 \theta+b^2 \cos^2 \theta}$. Then $M-m=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module