Equations involving sinx + cosx and sinx.cosx

Q.

If sin x + cos x = t, then sin x cos x is equal to

1. 

2. 

3. 

4. 

Q.

The number of solutions of equation, sin5x cos 3x = sin 6x cos 2x, in the

interval [0, $\pi$] are

1. 3

2. 4

3. 5

4. 6

Q.

What is the principal solution of 2 sin x = 1?

1. $x=\frac{\pi }{6}$

2. $x=\frac{\pi }{4}$

3. $x=\frac{\pi }{3}$

4. $x=\frac{\pi }{2}$

Q. The solution of the equation $[\sin x+\cos x{]}^{1+\sin 2x}=2,-\pi \le x\le \pi$ is

1. 
2. 
3. 
4. 
5. 

Q.

The general solution of $tanx=tan\alpha ,\alpha ϵ(-\frac{\pi }{2},\frac{\pi }{2})$ is

1. None of these

2. $x=n\pi +(-1{)}^n\alpha ,nϵZ$

3. $x=n\pi +\alpha ,nϵZ$

4. $x=2n\pi \pm \alpha ,nϵZ$

Q.

The general solution of the equation $si{n}^{50}x-co{s}^{50}x=1$ is

1. 

2. 

3. 

4. 

Q.

Find the general solution of 2sin 3x -1 =0

1. $x=n\pi +(-1{)}^n\frac{\pi }{18}$

2. $x=\frac{n\pi }{3}+(-1{)}^n\frac{\pi }{18}$

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

4. $x=\frac{n\pi }{3}+(-1{)}^n\frac{\pi }{18}$

Q.

Find the general solutions of $3tan\frac{x}{2}+3=0$

1. $x=2n\pi -\frac{\pi }{4}$

2. $x=2n\pi -\frac{\pi }{2}$

3. $x=n\pi -\frac{\pi }{2}$

4. $x=n\pi \pm \frac{\pi }{4}$

Q.

What is the principal solution of sin x = cos x ?

1. $x=-\frac{\pi }{6}$

2. $x=-\frac{\pi }{4}$

3. $x=\frac{\pi }{4}$

4. $x=\frac{\pi }{2}$

Q. If $x\ne \frac{n\pi }{2}$ and $(\cos x{)}^{{\sin }^{2}x-3\sin x+2}=1$ then all solutions of x are given by

1. 
2. None of these
3. 
4.