G Tewani Solutions for Chapter: Trigonometric Functions, Exercise 2: DPP

The number of value/values of $x$ for which $\sin y=x^2-2x$ is possible

Which of the following is not correct ?

If ${\sin }^4\alpha +{\cos }^4\beta +2=4\sin \alpha \cos \beta , 0 \le \alpha ,\mathit{ }\beta \le \frac{\mathrm{\pi }}{2}$ , then $\left(\sin \alpha +\cos \beta \right)$ is equal to

The number of ordered pairs $(a, x)$ satisfying the equation ${\sec }^2(a+2)x+a^2-1=0, -\pi <x<\pi$ is/are

The range of $y={\sin }^{3}x-6{\sin }^{2}x+11\sin x-6$ is

Let $f\left(x\right)=a\sin x+c,$ where $a$ and $c$ are real numbers and $a>0\mathrm{.}$ Then $f\left(x\right)<0,\forall x\in R$, if

Sum of maximum and minimum value of the function $f\left(x\right)={\sin }^{2}x+8\cos x-7$ is

${\theta }_1, {\theta }_2, {\theta }_3$ are angles of $1^{\mathrm{st}}$ quadrant, if $\tan {\theta }_1=\cos {\theta }_1, \tan {\theta }_2=\mathrm{cosec}{\theta }_2, \cos {\theta }_3={\theta }_3\mathrm{.}$ Which of the following is not true?