List of top Mathematics Questions on Trigonometric Functions asked in WBJEE

Evaluate the limit \[ \lim_{x \to 0} \frac{\tan \left( -\pi^2 x^2 - x^2 \tan \left( -\pi^2 \right) \right)}{\sin^2 x} \] is:

If \(\frac{1}{6}\)sinθ.cosθ.tanθ are in G.P, then the solution set θ is

The value of cos $15^{\circ}\, cos 7 \frac{1^{\circ}}{2}\, sin 7 \frac{1^{\circ}}{2}$ is

If $\theta \in\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right)$, then the value of $\sqrt{4 \cos ^{4} \theta+\sin ^{2} 2 \theta}+4 \cot \theta \cos ^{2}\left(\frac{\pi}{4}-\frac{\theta}{2}\right)$

The number of real solutions of the equation $(\sin x-x)\left(\cos x-x^{2}\right)=0$ is

Let $f(?) = (1+sin^2?)(2-sin^2?)$. Then for all values of $?$

Let $p, q$ and $r$ be the side4s opposite to the angles $P, Q$ and $R$, respectively in a $\Delta P Q R$. Then, $2 p r \sin \left(\frac{P-Q+R}{2}\right)$ equals

Let $p, q$ and $r$ be the sides opposite to the angles $P, Q$ and $R$, respectively in a $\Delta P Q R$. If $r^{2} \sin P \sin Q=p q$, then the triangle is

The number of solutions of $2\,\sin x + \cos\, x = 3$ is

Let $\tan \,\alpha = \frac{a}{a+1}$ and $\tan \,\beta = \frac{1}{2a + 1}$ then $\alpha + \beta$ is

If sin $\theta = \frac{2t}{1+t^{2}}$ and $?$ lies in the second quadrant, then $cos\,\theta$ is equal to

If $\theta + \phi = \frac{\pi}{4}$, then $\left(1+ \tan\,?\right)\left(1+ \tan\,\phi\right)$ is equal to

The value of $\cos\, 15^{\circ} - \sin \,15^{\circ}$ is

In a triangle $ABC$, if sin A sin $B =\frac{ab}{c^{2}}$, then the triangle is

The value of $\cos \frac{\pi}{15}\, \cos \frac{2\pi}{15}\, \cos \frac{4\pi}{15}\, \cos \frac{8\pi}{15} $ is

$$\begin{array}{l}\text{ Given: }\left|\begin{array}{ccc}a& b& a\alpha +b\\ b& c& b\alpha +c\\ ac+b& bc+c& 0\end{array}\right|=0\\ \text{ Applying }{C}_3\to C_3-(\alpha C_1+C_2)\end{array}$$If the determinant $\left|\begin{array}{ccc}a& b& 0\\ b& c& 0\\ a\alpha +b& bc+c& -(a{c}^2+2bc+c)\end{array}\right|=0$$$\Rightarrow -(a{\alpha }^2+2b\alpha +c)(ac-b^2)=0$$$$\Rightarrow a{\alpha }^2+2b\alpha +c=0\text{ or }{b}^2=ac$$$\therefore \alpha$ is root of $a{x}^2+2bx+c$ or $a,b,c$ are in GP.

Directions: The following question has four choices, out of which one or more are correct.A ray of light is incident on a reflecting surface. The ray moves in horizontal direction and is reflected vertically after striking the surface. If the surface is denoted by $y=\frac{2L}{\pi }\sin \left(\frac{\pi }{L}x\right),0\le x\le L,$ what are the coordinates of the point(s) where the ray is incident?

Directions: The following question has four choices, out of which one or more are correct.Let $\alpha =a\hat{i}+b\hat{j}+c\hat{k},\beta =b\hat{i}+c\hat{j}+a\hat{k}$ and $y=c\hat{i}+a\hat{j}+b\hat{k}$ be three co-planar vectors with $a\ne b$ and$v=\hat{i}+\hat{j}+\hat{k},$ Then $v$ is perpendicular to

An integrating factor of the differential equation $x\frac{dy}{dx}+y\log x=x{e}^x{x}^{-\frac{1}{2}\log x},(x>0)$