Question

The value of $\cot \frac{\pi }{24}$ is:

JEE Main 2021 (25 Jul Shift 2)

Options

• A: $\sqrt{2}+\sqrt{3}+2-\sqrt{6}$
• B: $\sqrt{2}+\sqrt{3}+2+\sqrt{6}$
• C: $\sqrt{2}-\sqrt{3}-2+\sqrt{6}$
• D: $3\sqrt{2}-\sqrt{3}-\sqrt{6}$

Question

$cosec18°$ is a root of the equation:

JEE Main 2021 (31 Aug Shift 1)

Options

• A: $x^2-2x-4=0$
• B: $4x^2+2x-1=0$
• C: $x^2+2x-4=0$
• D: $x^2-2x+4=0$

Question

The number of integral values of $k$ for which the equation $3\sin x+4\cos x=k+1$ has a solution, $k\in R$ is _______.

JEE Main 2021 (26 Feb Shift 1)

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Question

The value of $2\sin \frac{\pi }{22}\sin \frac{3\pi }{22}\sin \frac{5\pi }{22}\sin \frac{7\pi }{22}\sin \frac{9\pi }{22}$ is equal to:

JEE Main 2022 (25 Jul Shift 2)

Options

• A: $\frac{1}{16}$
• B: $\frac{5}{16}$
• C: $\frac{7}{16}$
• D: $\frac{3}{16}$

Question

If ${\sin }^2\left(10°\right)\sin \left(20°\right)\sin \left(40°\right)\sin \left(50°\right)\sin \left(70°\right)=\alpha -$ $\frac{1}{16}\sin \left(10°\right)$, then $16+{\alpha }^{-1}$ is equal to _____.

JEE Main 2022 (26 Jun Shift 1)

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Question

If the value of $\frac{3 \cos 36^{\circ}+5 \sin 18^{\circ}}{5 \cos 36^{\circ}-3 \sin 18^{\circ}}$ is $\frac{a \sqrt{5}-b}{c}$, where $a, b, c$ are natural numbers and $\operatorname{gcd}(a, c)=1$, then $a+b+c$ is equal to :

JEE Main 2024 (08 Apr Shift 2)

Options

• A: 40
• B: 52
• C: 50
• D: 54

Question

Let $|\cos \theta \cos (60-\theta) \cos (60+\theta)| \leq \frac{1}{8}, \theta \epsilon[0,2 \pi]$. Then, the sum of all $\theta \epsilon[0,2 \pi]$, where $\cos 3 \theta$ attains its maximum value, is :

JEE Main 2024 (09 Apr Shift 1)

Options

• A: $15 \pi$
• B: $18 \pi$
• C: $6 \pi$
• D: $9 \pi$