Question

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

• A. True
• B. False

Answer 1

The correct option is B False

Given that equation is $si{n}^4\theta -2si{n}^2\theta -1=0$.Therefore,
$si{n}^2\theta =\frac{2\pm \sqrt{8}}{2}=1\pm \sqrt{2}$
But $si{n}^2\theta$ cannot be negative. Therefore,
$si{n}^2\theta =\sqrt{2}+1$
But as $-1\le sin\theta \le 1,\therefore si{n}^2\theta \ne \sqrt{2}+1$
Thus, there is no value of $\theta$ which satisfic the given equation.
Therefore, statement is false.