(C) Given equations are $\cos \theta = \frac{1}{\sqrt{2}}$ and $\tan \theta = -1$ for $\theta \in [0, 2\pi]$.For $\cos \theta = \frac{1}{\sqrt{2}}$,th

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(C) Given equations are $\cos \theta = \frac{1}{\sqrt{2}}$ and $\tan \theta = -1$ for $\theta \in [0, 2\pi]$.For $\cos \theta = \frac{1}{\sqrt{2}}$,the possible values of $\theta$ are $\frac{\pi}{4}$ and $\frac{7\pi}{4}$.For $\tan \theta = -1$,the possible values of $\theta$ are $\frac{3\pi}{4}$ and $\frac{7\pi}{4}$.The common value satisfying both equations is $\theta = \frac{7\pi}{4}$.

Class 11 Mathematics Trigonometrical Equations Mix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance

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The value of $\theta$,satisfying both the equations $\cos \theta = \frac{1}{\sqrt{2}}$ and $\tan \theta = -1$ in the interval $[0, 2\pi]$,is

MHT CET 2022 All MHT CET

A
$\frac{\pi}{4}$
B
$\frac{5\pi}{4}$
C
$\frac{7\pi}{4}$
D
$\frac{3\pi}{4}$

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Trigonometrical Equations

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Mix Examples-Trigonometrical Equations and Inequations, Properties of Triangles, Height and Distance

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In a $\triangle PQR$,$m \angle R = \frac{\pi}{2}$. If $\tan \left(\frac{P}{2}\right)$ and $\tan \left(\frac{Q}{2}\right)$ are the roots of the equation $ax^2 + bx + c = 0$ $(a \neq 0)$,then:

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In a $\Delta ABC$,${a^2}\sin 2C + {c^2}\sin 2A = $

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In a triangle $ABC$,angle $A$ is greater than angle $B$. If the measures of angles $A$ and $B$ satisfy the equation $3\sin x - 4\sin^3 x - k = 0$ for $0 < k < 1$,then the measure of angle $C$ is:

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If the sides of a triangle $ABC$ whose perimeter is $42$ are in arithmetic progression,its circum-radius is $\frac{65}{8}$ and $B < A < C$,then $\sin A=$

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The sides of a triangle are $\sin \theta, \cos \theta$ and $\sqrt{1 + \sin \theta \cos \theta}$ for some $0 < \theta < \frac{\pi}{2}$. Then the greatest angle of the triangle is:

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The value of $\theta$,satisfying both the equations $\cos \theta = \frac{1}{\sqrt{2}}$ and $\tan \theta = -1$ in the interval $[0, 2\pi]$,is

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In a $\triangle PQR$,$m \angle R = \frac{\pi}{2}$. If $\tan \left(\frac{P}{2}\right)$ and $\tan \left(\frac{Q}{2}\right)$ are the roots of the equation $ax^2 + bx + c = 0$ $(a \neq 0)$,then:

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