Trigonometry Practice Test 1

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Question : 25 of 40

Marks: +1, -0

If

{\cosecθ+\sinθ}/{\cosecθ-\sinθ}=5/3

and

0° < θ < 90°,

what is the value of tan θ?

$1/2$
$1/ √3$
$√3$
$√ 3/2$
None of these

Solution:

{\cosecθ+\sinθ}/{\cosecθ-\sinθ}=5/3

⇒{1+\sin^2θ}/{1-\sin^2θ}=5/3

⇒{3+3\sin^2θ}={5-5\sin^2θ}

⇒8\sin^2θ=2

⇒\sin^2θ=1/4⇒\sinθ=1/2

⇒\sinθ=\sin30°⇒θ=30°

∴\tan30°=1/√3

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