General Solution of tan theta = tan alpha

Q.

What is the exact value of $\sec \left(45°\right)$?

Q.

Solve:$2co{s}^{2}x+3sinx=0$

Q.

The solution of the equation tan 2θ = tan 2/θ is

1. 

2. 

3. 

4. 

Q.

If α is the value of $xϵ[0,\pi ]$ satisfying 3 cos x + 3 sin x + sin 3x - cos 3x = 0, then find the value of $\frac{4\alpha }{\pi }$ ?

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Q.

How many values of $xϵ[0,2\pi ]$ satisfies the equation sin 2x + 5 sin x + 1 + 5 cos x = 0?

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Q. If $\exp \left[\right({\sin }^{2}x+{\sin }^{4}x+{\sin }^{6}x+....\infty ){\log }_{e}2$, satisfies the equation $x^2-9x+8=0$, then the value of $\frac{\cos x}{\cos x+\sin x},0<x<\frac{\pi }{2}$ is

1. $\frac{\sqrt{3}-1}{2}$
2. $\frac{\sqrt{3}+1}{2}$
3. $\sqrt{3}$
4. $-\sqrt{3}$

Q.

A circle with centre at the origin and radius equal to a meets the axis of x and A and B. $P\left(\alpha \right)$ and $Q\left(\beta \right)$ are two points on this circle so that $\alpha -\beta =2\gamma$, where $\gamma$ is a constant. The locus of the point of intersection of AP and BQ is

1. 
2. 
3. 
4. 

Q.

Find the principal and general solutions of the following equations.
cot x =$-\sqrt{3}$

Q.

Find the principal and general solutions of the following equation.

tan x = $\sqrt{3}$

Q.

What is the value of cos 25⁰ - cos35⁰?

1. -2sin5⁰

2. 2sin 5⁰

3. 1

4. 0

Q.

Find the general solution for the following equation:
sin 2x + cos x = 0

Q.

Find the general solution of the equation $sinmx+sinnx=0$

Or

Find the general solution of the equations $sin2x+sin4x+sin6x=0$

Q. $If4co{s}^{2}xsinx-2si{n}^{2}x=3sinx,thenx=\left(nϵZ\right)$

1. 
2. 
3. 
4. 

Q.

Find the value of $\theta$, if the equation $cos\theta x^2-2sin\theta x-cos\theta =0$ real root.

1. π/4

2. π/2

3. -π/4

4. -π/3

Q. If $\exp \left[\right({\sin }^{2}x+{\sin }^{4}x+{\sin }^{6}x+....\infty ){\log }_{e}2$, satisfies the equation $x^2-9x+8=0$, then the value of $\frac{\cos x}{\cos x+\sin x},0<x<\frac{\pi }{2}$ is

1. $\frac{\sqrt{3}-1}{2}$
2. $-\sqrt{3}$
3. $\frac{\sqrt{3}+1}{2}$
4. $\sqrt{3}$

Q.

"$$\begin{array}{cc}TrigonometricEquations& GeneralSolutions\\ 1.7co{s}^{2}x+si{n}^{2}x=4& P.n\pi \pm \frac{\pi }{4},wheren\in I\\ 2.si{n}^{2}x=\frac{1}{2}& Q.n\pi \pm \frac{\pi }{3},wheren\in I\\ 3.ta{n}^{2}x+3=0& R.n\pi \pm \frac{\pi }{6},wheren\in I\\ 4.3ta{n}^{2}x-1=0& S.Nosolution\end{array}$$ "

1. 1 - R, 2 - R, 3 - Q, 4 - R

2. 1 - R, 2 - P, 3 - S, 4 - P

3. 1 - Q, 2 - P, 3 - S, 4 - R

4. 1 - Q, 2 - P, 3 - Q, 4 - R

Q. 8. sec2 2x1- tan 2x

Q. The solution of equation 2cos^-1(x) +sin^-1(x) = 11π/6

Q. If $\frac{\tan 3\theta -1}{\tan 3\theta +1}=\sqrt{3}$, then the general value of $\theta$ is

1. $\frac{n\pi }{3}-\frac{\pi }{2}$
2. $n\pi +\frac{7\pi }{2}$
3. $\frac{n\pi }{3}-\frac{7\pi }{36}$
4. $n\pi +\frac{\pi }{12}$

Q. Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].

Q. Solve the trigonometric equation: 4^{†an^2x}-2^{sec^2x}+1=0, x∈\lbrack0, 20\rbrack

Q. Q.3 If k ∈ N is a divisor of n! + 1, then the number of values of k satisfying 2 < k < n, is/ar

Q. General solution of $\tan 5\mathrm{\theta }=\cot 2\mathrm{\theta }$ is
(a) $\frac{n\pi }{7}+\frac{\pi }{2},n\in Z$

(b) $\mathrm{\theta }=\frac{n\pi }{7}+\frac{\pi }{3},n\in Z$

(c) $\mathrm{\theta }=\frac{n\pi }{7}+\frac{\pi }{14},n\in Z$

(d) $\mathrm{\theta }=\frac{n\pi }{7}-\frac{\pi }{14},n\in Z$

Q. The number of distinct real roots of $\left|\begin{array}{ccc}sinx& cosx& cosx\\ cosx& sinx& cosx\\ cosx& cosx& sinx\end{array}\right|=0$ in the interval $-\frac{\pi }{4}\le x\le \frac{\pi }{4}$ is

1. 0
2. 2
3. 1
4. 3

Q. Match the equations with their general solutions. ($n\in I$)

1. $n\pi +{\tan }^{-1}2$
2. nπ+(-1)nπ3
3. 2nπ±2π3
4. $n\pi -\frac{\pi }{4}$

Q. If$\frac{sin(x+y)}{sin(x-y)}=\frac{a+b}{a-b}\text{then}\frac{tanx}{tany}=$

1. 
2. 
3. 
4. 

Q.

Solve for x, $2si{n}^{3}x=cosx$.

1. nπ, n ∈ I

2. 

3. 

4. 

Q.

Find the general solution of the equation:
4 sin x cos x + 2 sin x + 2 cos x + 1 = 0

Q. cos 2x + a sin x = 2a – 7 has a solution if

1. a = 0
2. 
3. 
4. 

Q. If $\frac{\tan 3\theta -1}{\tan 3\theta +1}=\sqrt{3}$, then the general value of $\theta$ is

1. 
2. 
3. 
4.