Trigonometry Practice Test 1

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Question : 15 of 40

Marks: +1, -0

If

{\sin θ}/{1+\cos θ}+{1+\cos θ}/{\sinθ}=4

, then what is the value of θ, where

0 ≤ θ ≤ π/2?

30°
45°
60°
90°
None of these

Solution:

Given that

{\sin θ}/{1+\cos θ}+{1+\cos θ}/{\sinθ}=4

⇒{\sin^2θ+(1+\cos θ)^2}/{(1+\cos θ)(\sinθ)}=4

⇒{\sin^2θ+\cos ^2θ+1+2\cosθ}/{(1+\cos θ)(\sinθ)}=4

⇒{2(1+\cos θ) }/{(1+\cos θ)(\sinθ)}=4

⇒\sinθ=1/2=\sin30°

⇒θ=30°

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