MHT CET 2026 19th April Morning Shift | Trigonometric Equations Question 3 | Mathematics

Let $x \in [0, 6\pi]$ satisfy the equation $\cos x - \sin x = -1$. If $x = k\left(\dfrac{\pi}{3}\right)$ where $k \in N$, then find the number of possible values of $k$ is .....

$3$

$4$

$6$

$8$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

The general solutions of the equation $\tan ^2 \theta+\sec 2 \theta=1$ are

$\mathrm{n} \pi, \mathrm{n} \pi \pm \frac{\pi}{3}, \mathrm{n} \in \mathbb{Z}$

$\mathrm{n} \pi, \mathrm{n} \pi \pm \frac{\pi}{4}, \mathrm{n} \in \mathbb{Z}$

$\quad \frac{\mathrm{n} \pi}{4}, \frac{\mathrm{n} \pi}{4} \pm \frac{\pi}{3}, \mathrm{n} \in \mathbb{Z}$

$\quad \mathrm{n} \pi, \mathrm{n} \pi \pm \frac{\pi}{6}, \mathrm{n} \in \mathbb{Z}$

MHT CET 2025 26th April Morning Shift

MCQ (Single Correct Answer)

-0

If $\tan (\pi \cos \theta)=\cot (\pi \sin \theta)$, then $\sin \left(\frac{\pi}{4}+\theta\right)=$

$\frac{1}{2}$

$\frac{1}{\sqrt{2}}$

$\frac{1}{4}$

$\frac{1}{2 \sqrt{2}}$

MHT CET 2025 25th April Evening Shift

MCQ (Single Correct Answer)

-0

The common principal solution of the equations $\sin \theta=-\frac{1}{2}$ and $\tan \theta=\frac{1}{\sqrt{3}}$ is

$\frac{\pi}{6}$

$\frac{5 \pi}{6}$

$\frac{7 \pi}{6}$

$\frac{11 \pi}{6}$

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