General Solution of Cos theta = Cos alpha

Q.

Total number of solutions of equation sin x tan 4x = cos x belonging to $(0,\pi )$ are:

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Q. If $\sin 3\theta =\sin \theta ,$ how many solutions exist such that $-2\pi <\theta <2\pi$ ?

1. 8
2. 9
3. 5
4. 7

Q.

Find the general solution for the following equation:

sin x + sin 3x + sin 5x = 0

Q. The general solution of the equation $\cos x=\frac{1}{\sqrt{2}}$ is x= .

1. 2nπ±π4
2. nπ+-1nπ4
3. nπ±π4

Q.

Find the general solution of the equation $sin7\theta =sin3\theta +sin\theta$

1. 

2. 

3. 

4. 

Q.

Find number of value of $xϵ[0,\pi ]$ satisfying the relation cos 3x + sin 2x - sin 4x = 0

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Q.

If the equation $2\cos x+\cos 2\lambda x=3$ has only one solution, then $\lambda$ is

1. $1$
2. a rational number
3. an irrational number
4. None of these

Q.

The product of the sines of the angles of a ΔABC is ϕ and the product of their cosines is q. Then the tangent of the angles is the roots of the equation

1. None of these

2. 

3. 

4. 

Q.

If ${\alpha }_0,{\alpha }_1,{\alpha }_2,.........{\alpha }_{n-1}$ be the n, $n^{th}$ roots of unity, then value of $\sum _{i=0}^{n-1}$ $\frac{{\alpha }_i}{(3-{\alpha }_i)}$ is equal to

1. $\frac{n}{3^n-1}$

2. $\frac{n-1}{3^n-1}$

3. $\frac{n+2}{3^n-1}$

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

Q.

How many values of $\theta ϵ[0,\frac{\pi }{2}]$, satisfy the relation cos $\theta +cos3\theta +cos5\theta +cos7\theta =0$ ?

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Q.

If tan A and tan B are the roots of the quadratic equation $x^2$ -ax+b=0, then the value of $si{n}^2$ (A+B) is

1. 

2. 

3. 

4. 

Q.

$Cos\theta +cos3\theta +cos5\theta +cos7\theta =4cos\theta cos2\theta cos4\theta$

1. True

2. False

Q.

Solve $\sqrt{2}secx+tanx=1$

Q.

How many values of $\theta ϵ[0,\frac{\pi }{2}]$, satisfy the relation cos $\theta +cos3\theta +cos5\theta +cos7\theta =0$ ?

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Q.

If ${\alpha }^2$ - (11 - i)$\alpha$ + 24 + 3$\beta$i = 0.Find the values of $\beta$.

1. 1, 8/3

2. 2, 8/3

3. 3, 8/3

4. 3, 1

Q. $cos(\alpha -\beta )=1$ and $cos(\alpha +\beta )=\frac{1}{e}$, where $\alpha ,\beta \in [-\pi ,\pi ]$. Number of pairs of $\alpha ,\beta$ which satisfy both the equation is

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

Q. Solve $3x+8>2,$ when (i) $x$ is an integer. (ii) $x$ is a real number

Q.

Total number of solutions of equation sin x tan 4x = cos x belonging to $(0,\pi )$ are:

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Q.

Solve $2{\cos }^2\theta +\cos \theta -1=0$

1. $2n\pi \forall n\in N$

2. $2n\pi \mp \frac{\pi }{3}\forall n\in N$

3. $2n\pi \mp \frac{\pi }{6}\forall n\in N$

4. $(2n+1)\frac{\pi }{6}\forall n\in N$

Q.

Find the general solution of each equation:

$\left(i\right)\sqrt{3}cotx+1=0$

$\left(ii\right)cosecx+\sqrt{2}=0$

Q.

Cos 4x cos 8x - cos 5x cos 9x = 0 if

1. Cos 12x = cos 14x

2. Sin 13x = 0

3. Sin x = 0

4. Cos x = 0

Q.

Find the general solution of (2 sin x - cos x) (1 + cos x) = $si{n}^2$ x

1. +

2. (2n + 1)

3. 2n

4. +

Q.

Solve $1+\cos x={\sin }^{2}x$

1. $(2n+1)\frac{\pi }{2}\forall n\in N$

2. $2n\pi \forall n\in N$

3. $(2n+1)\pi \forall n\in N$

4. $n\pi \forall n\in N$

Q. If $3\cos x\ne 2\sin x$, then the general solution of ${\sin }^{2}x-\cos 2x=2-\sin 2x$ is

1. 
2. 
3. 
4.