First slide

Compound angles

Question

If $\tan θ + \tan ϕ = a, \cot θ + \cot ϕ = b, θ - ϕ = α (\neq 0)$ then

Moderate

A

$a b < 4$
B

$a b = 4$
C

$a b > 4$
D

$a b = 0$

Solution

$\begin{array}{l} \frac{a}{b} = \tan θ \tan ϕ, \tan^{2} α = \tan^{2} (θ - φ) \\ = {(\frac{\tan θ - \tan ϕ}{1 + \tan θ \tan ϕ})}^{2} \end{array}$
$= \frac{a^{2} - 4 (a / b)}{(1 + (a / b)^{2}} = \frac{a b (a b - 4)}{(a + b)^{2}}$
Since $\tan^{2} a > 0, a b > 4$

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