SSC CGL Model Paper 7

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Question : 70 of 100

Marks: +1, -0

If

\sinθ= 5\sin(θ+ 2α)

, then

{\tan(θ+α)}/{\tanα}=?

$2/3$
$-2/3$
$-3/2$
$3/2$

Solution:

ATQ,

\Sinθ= 5\sin(θ+ 2α)

⇒

{\sinθ}/{\sin(θ+ 2α)}=5/1

Applying C - D rule
⇒

{ \sinθ+\sin(θ+ 2α)}/{ \sinθ-\sin(θ+ 2α)}={5+1}/{5-1}=6/4

⇒

{2 \sin({θ+θ+2α}/2).\cos({θ-θ-2α}/2)}/{2.\cos({θ+θ+2α}/2).\sin({θ-θ-2α}/2)}

=3/2

⇒

{\sin(θ+ α).\cos(-α)}/{\cos(θ+ α).\sin(-α) }=3/2

⇒

2{\tan(θ+α)} =-3\tanα

⇒

{\tan(θ+α)}/{\tanα}=-3/2

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