If cos⁡(x−y),cos⁡x and cos⁡(x+y) are in H.P. then value of cos⁡xsec⁡(y/2) is

A
$\pm \sqrt{2}$
B
$\pm \sqrt{3}$
C
$\pm 2$
D
$\pm 1$

Solution:

$\begin{array}{l} \frac{2}{\cos x} = \frac{1}{\cos (x - y)} + \frac{1}{\cos (x + y)} \\ \Rightarrow 2 (\cos^{2} x - \sin^{2} y) = 2 \cos x \cos x \cos y \\ \Rightarrow \cos^{2} x (1 - \cos y) = \sin^{2} y = 1 - \cos^{2} y \\ \Rightarrow \cos^{2} x = 1 + \cos y = 2 \cos^{2} (\frac{y}{2}) \\ \Rightarrow \cos x \sec (\frac{y}{2}) = \pm \sqrt{2} \end{array}$

NCERT Books for Class 12- Download Free PDF (2023-2024)

NCERT Books for Class 6 to 12 – Download Free PDF Updated for 2023-24

Learning Beyond Boundaries: Rohit Sharma’s Vision for Accessible Education

Rohit Sharma: The Cricketer, The Icon – A Biography

ORS Full Form – Oral Rehydration Solution

SDO Full Form – Sub Divisional Officer

ESI Full Form – Employee State Insurance

NEET 2023 Result Date: Check Result, Download NEET UG Result PDF

ESIC Full Form – Employees’ State Insurance Corporation

If $\cos (x - y), \cos x$ and $\cos (x + y)$ are in H.P. then value of $\cos x \sec (y / 2)$ is

Solution:

Related content