If $\sin A+\sin B+\sin C=3$, then $\cos A+\cos B+\cos C$ is equal to

Important Questions on Trigonometric Functions and Equations

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Entrances Gallery>Q 52

If $\cos \alpha +2\cos \beta +3\cos \gamma =0, \sin \alpha +2\sin \beta +3\sin \gamma =0$ and $\alpha +\beta +\gamma =\mathrm{\pi }$, then $\sin 3\alpha +8\sin 3\beta +27\sin 3\gamma$ is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Entrances Gallery>Q 53

If $\cos A=m\cos B$ and $\cot \left(\frac{A+B}{2}\right)=\lambda \tan \left(\frac{B-A}{2}\right)$, then $\lambda$ is equal to 

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Entrances Gallery>Q 54

The least value of $3{\sin }^2\theta +4{\cos }^2\theta$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Entrances Gallery>Q 55

If $\sin 2x=4\cos x,$ then $x$ is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Entrances Gallery>Q 56

Number of solutions of the equation $\tan x+\sec x=2\cos x,x\in \left[0,\pi \right]$ is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Entrances Gallery>Q 57

The value of $\theta$ satisfying $\cos \theta +\sqrt{3}\sin \theta =2$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Entrances Gallery>Q 58

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

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 9 - Trigonometric Functions and Equations>Entrances Gallery>Q 59

If $\sin \theta =3\sin \left(\theta +2\alpha \right)$, then the value of $\tan \left(\theta +\alpha \right)+2\tan \alpha$ is