Question

If $\sin\ \lbrack(2n + 1)\ \pi - \alpha\rbrack$, then the value of $= \sin(2n\pi + \pi - \alpha)$ is.

• A. $\sin(\pi - \alpha) = \sin\alpha$ or 1
• B. $\cos x - \sin x = \frac{1}{\sqrt{2}}$ or $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}\cos x - \frac{1}{\sqrt{2}}\sin x = \frac{1}{2}$ or $\cos\left( \frac{\pi}{4} + x \right) = \cos\frac{\pi}{3}$
• D. $\frac{\pi}{4} + x = 2n\pi \pm \frac{\pi}{3}$

Answer 1

Answer: (C)

$\frac{1}{\sqrt{2}}\cos x - \frac{1}{\sqrt{2}}\sin x = \frac{1}{2}$ or $\cos\left( \frac{\pi}{4} + x \right) = \cos\frac{\pi}{3}$

Answer 2

$\cot A,\cot B$

$\cot C$

$\cot A + \cot C = 2\cot B$

$\frac{\cos A}{\sin A} + \frac{\cos C}{\sin C} = \frac{2\cos B}{\sin B}$

$\frac{b^{2} + c^{2} - a^{2}}{2bc(ka)} + \frac{a^{2} + b^{2} - c^{2}}{2ab(kc)} = 2\frac{a^{2} + c^{2} - b^{2}}{2ac(kb)}$

$a^{2} + c^{2} = 2b^{2}$; ∴ $a^{2},b^{2},c^{2}$.