General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2

Q.

There exists a value of $\theta$ between 0 and $2\pi$ that satisfies the equation ${\sin }^4\theta -2{\sin }^2\theta -1=0.$

1. True
2. False

Q.

Statement (1): Maximum value of $si{n}^2$x + $co{s}^2$y is 2

Statement (2): Maximum value of 2 $se{c}^2$z is 2

1. Both the statements are correct

2. Only (1) is correct

3. Both the statements are wrong.

4. Only (2) is correct

Q.

If ${\sin }^{2}x$ + ${\cos }^{2}y$ = 2 ${\sec }^{2}z$, find the value of ${\cos }^{2}x$ + $si{n}^{2}y+2si{n}^{2}z$.

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Q.

How many values of $x$ in the interval $[0,2\pi ]$ satisfies the equation ${\sin }^{6}x=1+{\cos }^{4}3x$

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Q. The solutions of the equation $4{\cos }^{2}x+6{\sin }^{2}x=5$ are

1. 
2. 
3. 
4. 

Q.

If $si{n}^2$z = 1 + $co{s}^2$ y, find the value of $co{s}^2$ z + $si{n}^2$ y

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Q. In the interval $[0,\frac{\pi }{2}],$ the equation ${\log }_{\sin \theta }\left(\cos 2\theta \right)=2$ has

1. no solution
2. a unique solution
3. two solution
4. infinitely many solutions
   

Q. $\{x\in R:\cos 2x+2{\cos }^{2}x=2\}$ is equal to

1. 
2. 
3. 
4. 

Q.

If $\alpha$ is the value of $xϵ[0,2\pi ]$ which is a solution of the equation

$2co{s}^2$ $\frac{x^2+x}{6}=2^x$ + $2^{-x}$, then find the value of $\frac{2\alpha }{3\pi }$ .

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Q. The solutions of the equation $4{\cos }^{2}x+6{\sin }^{2}x=5$ are

1. 
2. 
3. 
4.