Trigonometry Practice Test 1

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Question : 9 of 40

Marks: +1, -0

p=√{{1-\sin x}/{1+\sin x}},q={1-\sin x}/{\cos x}

,

r={\cos x}/{1+\si x}

Which one of the following is correct?

p = q ≠ r
q = r ≠ p
r = p ≠ q
p = q = r
None of these

Solution:

p=√{{1-\sin x}/{1+\sin x}}

=√{{(1-\sin x)^2}/{1-\sin^2x}}

=√{{(1-\sin x)^2}/{\cos^2x}}

={1-\sin x}/{\cos x}=q

Now,

q ={1-\sin x}/{\cos x}×{1+\sin x}/{1+\sin x}

={1-\sin^2x}/{\cos x(1+\sin x)}

={\cos x}/{1+\sin x}=r

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