Question

If w is a cube root of unity, then sin\left{ \left( \omega^{35} + \omega^{25} \right)\pi + \frac{\pi}{2} \right} + \cos\left{ \left( \omega^{10} + \omega^{23} \right)\pi - \frac{\pi}{4} \right} is-

• A. $\frac{2 + \sqrt{2}}{2}$
• B. $\frac{2 + \sqrt{2}}{\sqrt{2}}$
• C. – $\frac{(2 + \sqrt{2})}{2}$
• D. $\frac{2 - \sqrt{2}}{2}$

Answer 1

Answer: (C)

– $\frac{(2 + \sqrt{2})}{2}$

Answer 2

Sol. w³⁵ + w²⁵ = w² + w = –1 and w¹⁰ + w²³ = w + w² = –1

\ the given expression is sin $\left( - \frac{\pi}{2} \right)$ + cos $\left( - \frac{5\pi}{4} \right)$

= –1 – $\frac{1}{\sqrt{2}}$= – $\left( \frac{2 + \sqrt{2}}{2} \right)$