(D) The maximum value of the expression $f(x) = \sin x + \cos x$ is given by $\sqrt{a^2 + b^2}$ where $a=1$ and $b=1$. Thus,the maximum value is $\sqr

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(D) The maximum value of the expression $f(x) = \sin x + \cos x$ is given by $\sqrt{a^2 + b^2}$ where $a=1$ and $b=1$. Thus,the maximum value is $\sqrt{1^2 + 1^2} = \sqrt{2}$. Since $\sqrt{2} \approx 1.414$,which is less than $2$,the equation $\sin x + \cos x = 2$ can never be satisfied for any real value of $x$. Therefore,the equation has no solutions.

Class 11 Mathematics Trigonometrical Equations Solution of trigonometrical equations

Easy

The equation $\sin x + \cos x = 2$ has

A
One solution
B
Two solutions
C
Infinite number of solutions
D
No solutions

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Solution of trigonometrical equations

The smallest positive value of $x$ in degrees satisfying the equation $\tan(x+100^{\circ}) = \tan(x+50^{\circ}) \tan(x) \tan(x-50^{\circ})$ is (in $^{\circ}$)

DifficultMHT CET 2024

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MediumTS EAMCET 2025

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MediumMHT CET 2025

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The general solution of the trigonometric equation $(\sqrt{3}-1) \sin \theta + (\sqrt{3}+1) \cos \theta = 2$ is

DifficultAP EAMCET 2017

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The general value of $\theta$ satisfying the equation $2\sin^2 \theta - 3\sin \theta - 2 = 0$ is

Medium

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The equation $\sin x + \cos x = 2$ has

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The smallest positive value of $x$ in degrees satisfying the equation $\tan(x+100^{\circ}) = \tan(x+50^{\circ}) \tan(x) \tan(x-50^{\circ})$ is (in $^{\circ}$)

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