First slide

Graphs of trigonometric functions in trigonometry

Question

If $cos⁡α= \frac{1}{2} (x + \frac{1}{x}) and \cos β = \frac{1}{2} (y + \frac{1}{y}), (xy > 0)$ $; x, y, α, β, \in R$ then

Moderate

A

$\sin (α + β + γ) = \sin γ \forall γ \in R$
B

$\cos αcos β = 1 \forall α, β \in R$
C

$(\cos α + \cos β)^{2} = 4 \forall α, β \in R$
D

$\sin (α + β + γ) = \sin α + \sin β + \sin γ \forall a, b, γ \in R$

Solution

$\cos α = \frac{1}{2} (x + \frac{1}{x}) and \cos β = \frac{1}{2} (y + \frac{1}{y})$
since xy > 0, we have
$x + \frac{1}{x} \geq 2 or \leq - 2 and y + \frac{1}{y} \geq 2 or \leq - 2$
$\begin{array}{l} \Rightarrow \cos α = 1, \cos β = 1 - - - - (1) \\ or \cos α = - 1, \cos β = - 1 - - - - (2) \\ \cos αcos β = 1 \\ \Rightarrow α + β is an even multiple of π \\ (\cos α + \cos β)^{2} = 4 \\ \Rightarrow \sin (α + β + γ) = \sin (2 nπ + γ) = \sin γ \\ Also, \sin α = \sin β = 0 . \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App