Question

General solution of the equation $2\cos^{2}\theta - (\sqrt{2} + 1)\cos\theta - 1 + \frac{(\sqrt{2} + 1)}{\sqrt{2}} = 0$is.

• A. $\Rightarrow$
• B. $\cos\theta = \frac{(\sqrt{2} + 1) \pm \sqrt{(\sqrt{2} + 1)^{2} - \frac{8}{\sqrt{2}}}}{4}$
• C. $\Rightarrow$
• D. None of these

Answer 1

Answer: (B)

$\cos\theta = \frac{(\sqrt{2} + 1) \pm \sqrt{(\sqrt{2} + 1)^{2} - \frac{8}{\sqrt{2}}}}{4}$

Answer 2

On simplification, it reduces to

$\Rightarrow$

$\theta = 2n\pi \pm \frac{\pi}{3}$ $\sqrt{2}\sec\theta + \tan\theta = 1 \Rightarrow \frac{\sqrt{2}}{\cos\theta} + \frac{\sin\theta}{\cos\theta} = 1$.