Trigonometry Practice Test 1

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Question : 12 of 40

Marks: +1, -0

{\cosθ}/{1-\sin θ}-{\cosθ}/{1+\sinθ}=2

is satisfied by which one of the following values of θ?

$π/2$
$π/3$
$π/4$
$π/6$
None of these

Solution:

Given,

{\cosθ}/{1-\sin θ}-{\cosθ}/{1+\sinθ}=2

⇒{\cosθ+\sinθ\cosθ-\cosθ+\cosθ\sinθ}/{1-\sin^2θ}=2

⇒2\sinθ\cosθ=2\cos^2θ

⇒\sinθ=\cosθ

⇒\tanθ=1\and \cosθ≠0

⇒θ=π/4

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