General Solution of cos theta = cos alpha

Q. The general solution of $\sin 2x+\sin 4x+\sin 6x=0$ is/are

1. $n\pi \pm \frac{\pi }{6},n\in Z$
2. $\frac{n\pi }{4},n\in Z$
3. $2n\pi \pm \frac{2\pi }{3},n\in Z$
4. $n\pi \pm \frac{\pi }{3},n\in Z$

Q. If $4{\sin }^2\theta +2(\sqrt{3}+1)\cos \theta =4+\sqrt{3}$, then the general solution is

1. $n\pi \pm \frac{\pi }{3},n\in Z$
2. $n\pi \pm \frac{\pi }{6},n\in Z$
3. $2n\pi \pm \frac{\pi }{3},n\in Z$
4. $2n\pi \pm \frac{\pi }{4},n\in Z$

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

1. 8
2. 9
3. 11
4. 7

Q.

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

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Q. The number of solution(s) of $\sin 3x-\sin x=4{\cos }^{2}x-2$ for $x\in [0,2\pi ]$ is

1. $1$
2. $2$
3. More than $2$ but finite
4. infinitely many

Q. The sum of all the solutions of the equation $\cos \theta \cos (\frac{\pi }{3}+\theta )\cos (\frac{\pi }{3}-\theta )=\frac{1}{4},\theta \in [0,6\pi ]$ is

1. $15\pi$
2. $30\pi$
3. $\frac{100\pi }{3}$
4. None of these

Q. The general solution of $\sin 2x+\sin 4x+\sin 6x=0$ is/are

1. $n\pi \pm \frac{\pi }{6},n\in Z$
2. $\frac{n\pi }{4},n\in Z$
3. $2n\pi \pm \frac{2\pi }{3},n\in Z$
4. $n\pi \pm \frac{\pi }{3},n\in Z$

Q.

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

1. $n\pi$ + $(-1{)}^n$ $\frac{\pi }{6}$

2. (2n + 1)$\pi$

3. 2n$\pi$

4. $n\pi$ + $(-1{)}^n$ $\frac{\pi }{3}$

Q.

Evaluate: $\mathrm{cosec}\frac{-3\mathrm{\pi }}{4}$.

Q.

How do you use trigonometric identities to transform one side of the equation into the other $\cos \theta sec\theta =1$?

Q.

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

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Q. The general solution of the equation $\cos \theta =\cos \alpha$, is given by $\theta =n\pi \pm \alpha ,n\in Z.$

1. True
2. False

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

1. 8
2. 9
3. 11
4. 7

Q. If $3\sin x+4\cos ax=7$ has at least one solution and $a=\frac{pm}{qn+1};$ where $m,n\in Z,$ then the value of $p+q$ is

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. $cos(\alpha -\beta )=1$ 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. \N
2. 1
3. 2
4. 4

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

1. $n\pi +(-1{)}^n\frac{\pi }{2},n\in Z$
2. $\frac{n\pi }{2},n\in Z$
3. $(4n\pm 1)\frac{\pi }{2},n\in Z$
4. $(2n-1)\pi ,n\in Z$

Q. The general value of θ in the equation $\cos \theta =\frac{1}{\sqrt{2}},\tan \theta =-1$ is

1. $2n\pi \pm \frac{\pi }{6},n\in I$
2. $2n\pi \pm \frac{7\pi }{4},n\in I$
3. $n\pi +(-1{)}^n.\frac{\pi }{3},n\in I$
4. $n\pi +(-1{)}^n.\frac{\pi }{4},n\in I$

Q. General values of $x$ for which $\sin 2x+\cos x=0$ is/are :

1. $\frac{2n\pi }{3}+\frac{\pi }{6}$
2. $\frac{2n\pi }{3}-\frac{\pi }{6}$
3. $2n\pi +\frac{\pi }{2}$
4. $2n\pi -\frac{\pi }{2}$

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

1. $n\pi +(-1{)}^n\frac{\pi }{2},n\in Z$
2. $\frac{n\pi }{2},n\in Z$
3. $(4n\pm 1)\frac{\pi }{2},n\in Z$
4. $(2n-1)\pi ,n\in Z$