Statement $-1:$ The number of common solutions of the trigonometric equations $2\,sin^2\,\theta - cos\,2\theta = 0$ and $2 \,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, 2\pi ]$ is two.
Statement $-2:$ The number of solutions of the equation, $2\,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, \pi ]$ is two.
Statement $-1$ is true; Statement $-2$ is true;Statement $-2$ is a correct explanation for statement $-1.$
Statement $-1$ is true; Statement $-2$ is true;Statement $-2$ is not a correct explanation for statement $-1.$
Statement $-1$ is false; Statement $-2$ is true.
Statement $-1$ is true; Statement $-2$ is false.
The number of solutions of the equation $4 \sin ^2 x-4$ $\cos ^3 \mathrm{x}+9-4 \cos \mathrm{x}=0 ; \mathrm{x} \in[-2 \pi, 2 \pi]$ is :
The equation $\sqrt 3 \sin x + \cos x = 4$ has
Let $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\}$.
Then $\sum_{\theta \in S } \sin ^2\left(\theta+\frac{\pi}{4}\right)$ is equal to
Number of solution$(s)$ of the equation $ln(1 + sin^2x) = 1 -ln(5 + x^2)$ is -
The number of values of $x$ in the interval $[0, 5\pi]$ satisfying the equation $3sin^2x\, \,-\,\, 7sinx + 2 = 0$ is