Chapter 4
Comprehensive Trigonometry for IIT JEE Main and Advanced Rejaul Makshud MeGraw Hill · 45 exercises
Problem 1
Solve for \(x\) : $$ \frac{\sin x+\cos x}{\sin x-\cos x}>\sqrt{3} $$
3 step solution
Problem 1
\(\sin (3 x-1)>0\)
4 step solution
Problem 1
Solve for \(x\) : $$ \sin x>\frac{1}{2} $$
4 step solution
Problem 2
Solve for \(x\) : $$ |\sin x|>|\cos x| $$
3 step solution
Problem 2
\(\cos (2 x-3)<0\)
3 step solution
Problem 2
Solve for \(x\) : $$ \sin x \geq 1 $$
3 step solution
Problem 3
Solve for \(x\) : $$ \cot x+\frac{\sin x}{\cos x-2} \geq 0 $$
4 step solution
Problem 3
\(|\sin x| \leq \frac{1}{2}\)
4 step solution
Problem 3
Solve for \(x\) : $$ \sin x \leq \frac{1}{\sqrt{2}} $$
3 step solution
Problem 4
Solve for \(x\) : $$ \sin x+\cos x>\sqrt{2} \cos 2 x $$
4 step solution
Problem 4
\(|\cos x| \leq \frac{1}{\sqrt{2}}\)
4 step solution
Problem 4
Solve for \(x\) : $$ \sin x<\frac{\sqrt{3}}{2} $$
3 step solution
Problem 5
Solve for \(x\) : $$ 4 \sin x \sin 2 x \sin 3 x>\sin 4 x $$
4 step solution
Problem 5
\(|\sin 2 x+\cos 2 x|=|\sin 2 x|+|\cos 2 x|\)
3 step solution
Problem 5
Solve for \(x\) : $$ \cos x>\frac{\sqrt{3}}{2} $$
3 step solution
Problem 6
Solve for \(x\) : $$ \frac{\cos ^{2} 2 x}{\cos ^{2} x} \geq 3 \tan x $$
4 step solution
Problem 6
\(2 \cos ^{2} x+\cos x<1\)
5 step solution
Problem 6
Solve for \(x\) : $$ \cos x \geq \frac{1}{2} $$
3 step solution
Problem 7
Solve for \(x\) : $$ \frac{\cos x+2 \cos ^{2} x+\cos 3 x}{\cos x+2 \cos ^{2} x-1}>1 $$
3 step solution
Problem 7
\(4 \sin ^{2} x-1 \leq 0\)
3 step solution
Problem 7
Solve for \(x\) : $$ \cos x<\frac{1}{\sqrt{2}} $$
3 step solution
Problem 8
Solve for \(x\) : $$ 2(\sqrt{2}-1) \sin x-2 \cos 2 x+\sqrt{2}(\sqrt{2}-1)<0 $$
3 step solution
Problem 8
\(4 \cos ^{2} x-3 \geq 0\)
3 step solution
Problem 8
Solve for \(x\) : $$ \cos x<\frac{1}{3} $$
3 step solution
Problem 9
Solve for \(x\) : $$ \begin{aligned} &\sin 2 x>\sqrt{2} \sin ^{2} x+(2-\sqrt{2}) \cos ^{2} x \\ &, x \in(0,2 \pi) \end{aligned} $$
4 step solution
Problem 9
\(|\sin x|>|\cos x|\)
5 step solution
Problem 9
Solve for \(x\) : $$ \tan x>\frac{1}{\sqrt{3}} $$
2 step solution
Problem 10
Solve for \(x\) : $$ 1+\log _{4} \sin x+2 \log _{16} \cos x>0 $$
5 step solution
Problem 10
\(|\cos x|>|\sin x|\)
3 step solution
Problem 10
Solve for \(x\) : $$ \tan x \geq 1 $$
3 step solution
Problem 11
\(\sin x+\cos x-\cos 2 x>0\)
5 step solution
Problem 11
Solve for \(x\) : $$ \sin 2 x<\frac{1}{2} $$
3 step solution
Problem 12
\(x^{2}+x-2<0\) and \(\sin x>\frac{1}{2}\)
3 step solution
Problem 12
Solve for \(x\) : $$ \sin 3 x<\frac{\sqrt{3}}{2} $$
3 step solution
Problem 13
\(x^{2}-1 \leq 0\) and \(\cos x<\frac{1}{2}\)
3 step solution
Problem 13
Solve for \(x\) : $$ \cos 5 x \geq \frac{1}{2} $$
3 step solution
Problem 14
\(4 x^{2}-1 \geq 0\) and \(\tan x \geq \frac{1}{\sqrt{3}}\)
4 step solution
Problem 14
Solve for \(x\) : $$ \sin x+\cos x>1 $$
3 step solution
Problem 15
\(x^{2}-3 x+2<0\) and \((\sin x)^{2}-\sin x>0\)
2 step solution
Problem 15
Solve for \(x\) : $$ \sin x-\cos x<1 $$
5 step solution
Problem 16
Solve for \(x\) : $$ \sqrt{3} \sin x+\cos x>1 $$
2 step solution
Problem 17
Solve for \(x\) : $$ \sin x-\sqrt{3} \cos x<1 $$
3 step solution
Problem 18
Solve for \(x\) : $$ \sin ^{2} x+\sin x-2<0 $$
3 step solution
Problem 19
Solve for \(x\) : $$ \sin ^{2} x+3 \sin x+2<0 $$
3 step solution
Problem 20
Solve for \(x\) : $$ \cos ^{2} x-\cos x>0 $$
4 step solution