This chapter is currently out of syllabus
1
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

The sum of the solutions $$x \in \mathbb{R}$$ of the equation $$\frac{3 \cos 2 x+\cos ^3 2 x}{\cos ^6 x-\sin ^6 x}=x^3-x^2+6$$ is

A
3
B
1
C
0
D
$$-$$1
2
JEE Main 2024 (Online) 29th January Morning Shift
+4
-1

If $$\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}$$ is the solution of $$4 \cos \theta+5 \sin \theta=1$$, then the value of $$\tan \alpha$$ is

A
$$\frac{10-\sqrt{10}}{12}$$
B
$$\frac{\sqrt{10}-10}{6}$$
C
$$\frac{\sqrt{10}-10}{12}$$
D
$$\frac{10-\sqrt{10}}{6}$$
3
JEE Main 2024 (Online) 27th January Evening Shift
+4
-1

If $$2 \tan ^2 \theta-5 \sec \theta=1$$ has exactly 7 solutions in the interval $$\left[0, \frac{n \pi}{2}\right]$$, for the least value of $$n \in \mathbf{N}$$, then $$\sum_\limits{k=1}^n \frac{k}{2^k}$$ is equal to:

A
$$\frac{1}{2^{14}}\left(2^{15}-15\right)$$
B
$$1-\frac{15}{2^{13}}$$
C
$$\frac{1}{2^{15}}\left(2^{14}-14\right)$$
D
$$\frac{1}{2^{13}}\left(2^{14}-15\right)$$
4
JEE Main 2023 (Online) 11th April Morning Shift
+4
-1
Out of Syllabus

The number of elements in the set

$$S=\left\{\theta \in[0,2 \pi]: 3 \cos ^{4} \theta-5 \cos ^{2} \theta-2 \sin ^{6} \theta+2=0\right\}$$ is :

A
9
B
8
C
12
D
10
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