Question
Download Solution PDFIf p tan (θ - 30°) = q tan (θ + 120°), then what is (p + q) / (p - q) equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
p tan (θ - 30°) = q tan (θ + 120°)
⇒ p\q = \(\frac{tan(\theta + 120°)}{tan(\theta -30°)}\)
= \(\frac{sin(\theta+120)cos(\theta -30)}{cos(\theta+120)sin(\theta-30)}\)
⇒ \(\frac{p+q}{p-q} = \)\(\frac{sin(\theta+120)cos(\theta -30)+cos(\theta+120)sin(\theta-30)}{sin(\theta+120)cos(\theta -30)-cos(\theta+120)sin(\theta-30)}\)
= \(\frac{sin[(\theta+120)+(\theta-30)]}{sin[(\theta+120)-(\theta-30)]}\)
= \(\frac{sin(90+2\theta)}{sin 150}\)
⇒ \(\frac{p+q}{p-q} = \frac{sin(90+2\theta)}{\frac{1}{2}}\)
= 2 cos2θ
∴ Option (d) is correct
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