Question

Help me with this question also​

Answer 1

`\text{Given that,}\\\\`

`~~~~~~~\cos \theta = \frac 89\\\\\\\implies 2\cos^2 \left(\frac{\theta}2 \right) -1 = \frac 89~~~~~~;\left[1+ \cos 2\theta = 2\cos^2 \theta \right]\\\\\\\implies 2 \cos^2 \left(\frac{\theta}2 \right)= \frac 89 +1\\\\\\\implies 2 \cos^2 \left(\frac{\theta}2 \right)=\frac{17}9\\\\\\\implies \cos^2 \left(\frac{\theta}2 \right) = (17)/(18)\\\\\\\implies \cos \left(\frac{\theta}2 \right)=\sqrt{(17)/(18)}~~~~~~~~~~~;\left[\text{Positive value of} ~\cos \left(\frac{\theta}2\right) \right]`

`\implies \cos \left(\frac{\theta} 2 \right) =(√(17))/(√(9 * 2))\\\\\\\implies \cos \left(\frac{\theta} 2 \right)=(√(17))/(3\sqrt 2)\\\\\\\implies \cos \left(\frac{\theta} 2 \right)=(√(17) \cdot \sqrt 2)/(3\cdot 2)\\\\\\\implies \cos \left(\frac{\theta} 2 \right)=(√(34))/(6 )`