Principal Solution of Trigonometric Equation

Q.

"$$\begin{array}{cc}\text{Trigonometric Equation}& \text{Principal Solutions}\\ 1.sinx=\frac{\sqrt{3}}{2}& A.\frac{5\pi }{6}\\ 2.tanx=\frac{-1}{\sqrt{3}}& B.\frac{5\pi }{12}\\ 3.sec2x=\frac{-2}{\sqrt{3}}& C.\frac{7\pi }{12}\\ 4.cos3x=\left(\frac{-1}{2}\right)& D.\frac{\pi }{3}\\ & E.\frac{2\pi }{9}\\ & F.\frac{4\pi }{9}\\ & G.\frac{11\pi }{6}\\ & H.\frac{2\pi }{3}\end{array}$$ "

1. 1 - d, 2 - a, 3 - b, 4 - e

2. 1 - d, 2 - g, 3 - b, 4 - f

3. 1 - h, 2 - a, 3 - c, 4 - j

4. 1 - h, 2 - g, 3 - c, 4 - e

Q. If $5\cos 2\theta +2{\cos }^2\frac{\theta }{2}=-1,$ when $(0<\theta <\pi ),$ then the values of $\theta$ are

1. 
2. 
3. 
4. 

Q.

Principal solutions are ______

1. The solutions of a trigonometric equation which lie in the interval [0, 2π]

2. The solutions of a trigonometric equation which lie in the interval [0, 2π)

3. The solutions of a trigonometric equation which lie in the interval [0, π)

4. The solutions of a trigonometric equation which lie in the interval [0, π]

Q.

The number of values of $\theta$ in the interval $(-\frac{\pi }{2},\frac{\pi }{2})$ such that $\theta \ne \frac{n\pi }{5}forn=0,\pm 1,\pm 2$ and $tan\theta =cot5\theta$ as well as $sin2\theta =cos4\theta$ is___

Q.

The set of positive real values of the parameter 'a' for which the equation |sin2x|-|x|-a=0 does not have any real solution is

1. $(\frac{3\sqrt{3}-\pi }{6},\infty )$

2. $(\frac{3\sqrt{3}-\pi }{12},\infty )$

3. $(\frac{3\sqrt{3}+\pi }{12},\infty )$

4. $(\frac{3\sqrt{3}+\pi }{6},\infty )$

Q. For $0<\theta <\frac{\pi }{2},$ the solution (s) of
${\sum }_{m=1}^{6}cosec(\theta +\frac{(m-1)\pi }{4})cosec(\theta +\frac{m\pi }{4})=4\sqrt{2}$ is/are

1. 
2. 
3. 
4. 

Q. If $0\le x<2\pi$ , then the number of real values of x, which satisfy the equation $\cos x+\cos 2x+\cos 3x+\cos 4x=0$, is

1. $3$
2. $9$
3. $5$
4. $7$

Q. The principal solution of a trigonometric equation lies in the interval

1. -π2, π2
2. $(-\pi ,\pi )$
3. $[0,2\pi )$

Q. The principal solution of the equation $\sin x=\frac{1}{2}$ that is less than $\frac{\pi }{2}$ is

1. $\frac{\pi }{3}$
2. $\frac{\pi }{3}$
3. $\frac{\pi }{6}$

Q.

Principal solutions are ______

1. The solutions of a trigonometric equation which lie in the interval [0, 2π]

2. The solutions of a trigonometric equation which lie in the interval [0, 2π)

3. The solutions of a trigonometric equation which lie in the interval [0, π)

4. The solutions of a trigonometric equation which lie in the interval [0, π]