NIMCET 2018 — Mathematics PYQ

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Question

NIMCET 2018 — Mathematics PYQ

NIMCET | Mathematics | 2018

If $sin θ = 3 sin (θ + 2α)$ , then the value of $tan (θ + α) + 2 tan α$ is

Choose the correct answer:

Explanation

Concept:
componendo and dividendo formula, we have
$\frac{a}{b} = \frac{a + b}{a - b}$
Trigonometric formula:
sin C + sin D = 2sin (C+D).sin (C - D)
sin C - sin D = 2sin (C+D).sin (C - D)
Calculations:
Given, sin θ = 3 sin (θ + 2α)
$</span><br><span style="font-size: 14pt;">\frac{\sin θ}{\sin (θ + 2α)} = \frac{3}{1}$
By componendo and dividendo formula, we have
$\frac{\sin θ + \sin (θ + 2α)}{\sin θ - \sin (θ + 2α)} = \frac{3+1}{3-1}$
We know that,

$sin$ C $+ sin$ D $= - 2 sin (C + D) . sin (C - D)$ $sin$ C- $sin$ D $= 2 sin (C + D) . sin (C - D)$

$\to - 2 sin (θ + 2 α)$ cos $α_{= 2}$

$2 cos (θ + 2 α) sin α$

$\Rightarrow - tan (θ + 2 α) cot α = 2$

$\Rightarrow - tan (θ + 2 α) = 2 tan α$

$\Rightarrow$ $tan$ $(θ + 2 α) + 2$ $tan$ $α = 0$

Choose the correct answer:

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