Let 2 and cot = - 1 2 2 . Then the value of sin ( 15 2 ) ( cos 8 + sin 8 ) + cos ( 15 2 ) ( cos 8 - sin 8 ) is equal to [2026]

Question

Let $\frac{π}{2} < θ < π$ and $\cot θ = - \frac{1}{2 \sqrt{2}}$ . Then the value of $\sin (\frac{15 θ}{2}) (\cos 8 θ + \sin 8 θ) + \cos (\frac{15 θ}{2}) (\cos 8 θ - \sin 8 θ)$ is equal to [2026]

Smart Achievers · Accepted Answer

(2)

$\frac{π}{2} < θ < π and \cot θ = - \frac{1}{2 \sqrt{2}}$

$\Rightarrow \sin (\frac{15 θ}{2}) (\cos 8 θ + \sin 8 θ) + \cos (\frac{15 θ}{2}) (\cos 8 θ - \sin 8 θ)$

$\Rightarrow \sin (\frac{15 θ}{2}) \cos 8 θ - \cos (\frac{15 θ}{2}) \sin 8 θ + \sin (\frac{15 θ}{2}) \sin 8 θ + \cos (\frac{15 θ}{2}) \cos 8 θ$

$\Rightarrow \sin (\frac{15 θ}{2} - 8 θ) + \cos (\frac{15 θ}{2} - 8 θ)$

$\Rightarrow \cos \frac{θ}{2} - \sin \frac{θ}{2} = - \sqrt{1 - \sin θ} (\frac{π}{4} < \frac{θ}{2} < \frac{π}{2})$

$\Rightarrow given \cot θ = - \frac{1}{2 \sqrt{2}}, \sin θ = \frac{2 \sqrt{2}}{3}$

$\Rightarrow - \sqrt{1 - \sin θ} = \sqrt{\frac{3 - 2 \sqrt{2}}{3}} = \frac{(\sqrt{2} - 1)}{3}$

$= \frac{1 - \sqrt{2}}{\sqrt{3}}$

Solution

Q.
Let $\frac{π}{2} < θ < π$ and $\cot θ = - \frac{1}{2 \sqrt{2}}$ . Then the value of $\sin (\frac{15 θ}{2}) (\cos 8 θ + \sin 8 θ) + \cos (\frac{15 θ}{2}) (\cos 8 θ - \sin 8 θ)$ is equal to [2026]

1 $\frac{\sqrt{2} - 1}{\sqrt{3}}$

2 $\frac{1 - \sqrt{2}}{\sqrt{3}}$

3 $- \frac{\sqrt{2}}{\sqrt{3}}$

4 $\frac{\sqrt{2}}{\sqrt{3}}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. Let π2<θ<π and cotθ=-122. Then the value of sin(15θ2)(cos 8θ+sin 8θ)+cos(15θ2)(cos 8θ-sin 8θ) is equal to [2026]

1 2-13

2 1-23

3 -23

4 23