Question

If cos (x – y), cos x and cos (x+ y) are in HP, then cos x sec$\left(\frac{y}{2}\right)$ is equal to

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

$Given,cos(x-y),cosx,cos(x+y)areinHP.\Rightarrow cosx=\frac{2cos(x-y)cos(x+y)}{cos(x-y)+cos(x+y)}\Rightarrow x=\frac{2(co{s}^{2}x-si{n}^{2}y)}{2cosxcosy}\Rightarrow co{s}^{2}x=1+cosy=2co{s}^2\frac{y}{2}\Rightarrow co{s}^{2}xse{c}^2\frac{y}{2}=2\Rightarrow cosxsec\frac{y}{2}=\pm \sqrt{2}$