The value of tan $5\theta$ is

Important Questions on Trigonometric Functions and Equations

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Work Book exercise 9.2>Q 16

If $\left|a{\sin }^2\theta +b\sin \theta \cos \theta +c{\cos }^2\theta -\frac{1}{2}\left(a+c\right)\right|\le \frac{1}{2}k$, then $k^2$ is equal to 

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Work Book exercise 9.2>Q 17

If $\alpha , \beta , \gamma$ and $\delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $\lambda ,$ then the value of $4\sin \frac{\alpha }{2}+3\sin \frac{\beta }{2}+2\sin \frac{\gamma }{2}+\sin \frac{\delta }{2}$ is 

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Work Book exercise 9.2>Q 18

If $\tan \left(\frac{\theta }{2}\right)=\frac{5}{2}$ and $\tan \left(\frac{\varphi }{2}\right)=\frac{3}{4},$ then the value of $\cos \left(\theta +\varphi \right)$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Work Book exercise 9.2>Q 20

If $\cos x=\tan y,\cos y=\tan z,\cos z=\tan x,$ then the value of $\sin x$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Work Book exercise 9.3>Q 1

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

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Work Book exercise 9.3>Q 2

If the equation $\left(\cos p-1\right)x^2+\left(\cos p\right)x+\sin p=0$, where $x$ is a variable, has real roots, then, all values of $p$ lies in the set $A$. Then a subset of $A$ is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Work Book exercise 9.3>Q 3

The smallest positive root of the equation $\tan x-x=0,$ lies in 

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Work Book exercise 9.3>Q 4

General solution of the equation $\left(\sqrt{3}-1\right)\sin \theta +\left(\sqrt{3}+1\right)\cos \theta =2$ is