The number of distinct real roots of the equation $x={\left(\frac{5\pi }{2}\right)}^{\cos x}$is:

Important Questions on Trigonometric Equations and Inequalities

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 5 - Trigonometric Equations and Inequalities>Exercise 1>Q 45

For $x\in \left(0,\mathrm{\pi }\right)$, the equation $\sin x+2\sin 2x-\sin 3x=3$ has

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 5 - Trigonometric Equations and Inequalities>Exercise 1>Q 46

If $0<x<\pi$ and $\cos x+\sin x=\frac{1}{2},$ then $\tan x$ is,

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 5 - Trigonometric Equations and Inequalities>Exercise 1>Q 47

If $\tan \theta +\sec \theta =\sqrt{3}$  and  $0<\mathrm{\theta }<\pi$, then $\theta$ is equal to

MEDIUM

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 5 - Trigonometric Equations and Inequalities>Exercise 1>Q 48

The set of all $x$ in $\left(\frac{-\pi }{2},\frac{\pi }{2}\right)$ satisfying $|4\sin x-1|<\sqrt{5}$ is given by

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 5 - Trigonometric Equations and Inequalities>Exercise 1>Q 49

If $\frac{\sin 3\theta }{\cos 2\theta }<0$, then $\theta$lies in:

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 5 - Trigonometric Equations and Inequalities>Exercise 1>Q 50

Let $\theta \in \left(0, \frac{\pi }{4}\right)$ and $t_1={\left(\tan \theta \right)}^{\tan \theta }, t_2={\left(\tan \theta \right)}^{\cot \theta }, t_3={\left(\cot \theta \right)}^{\tan \theta }$ and $t_4={\left(\cot \theta \right)}^{\cot \theta },$ then

HARD

Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 5 - Trigonometric Equations and Inequalities>Exercise 1>Q 51

If $0<\theta <2\pi ,$ then the intervals of values of $\mathrm{\theta }$ for which $2{\sin }^2\theta -5\sin \theta +2>0,$ is