Question
Download Solution PDFIf 2 cot θ = 3, then find the value of \(\frac{\sqrt{13} \sin \theta-3 \tan \theta}{3 \tan \theta+\sqrt{13} \cos \theta}\).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
2cotθ = 3
Formula used:
Sinθ = P/H
Cosθ = B/H
Tanθ = P/B
Cotθ = B/P
H2 = P2 + B2
where P = Perpendicular
B = Base
H = Height
Calculation:
2cotθ = 3
⇒ cotθ = 3/2
on comparing with (Cotθ = B/P), we get
⇒ B = 3
⇒ P = 2
According to Pythagorean theorem
⇒ H2 = P2 + B2
⇒ H2 = 22 + 32
⇒ H = √13
⇒ Sinθ = 2/√13
⇒ Cosθ = 3/√13
⇒ Tanθ = 2/3
Putting all the values in the given equation:
\(\frac{\sqrt{13} \sin \theta-3 \tan \theta}{3 \tan \theta+\sqrt{13} \cos \theta}\)= (√13 * 2/√13 - 3 * 2/3 )/ (3 * 2/3 + √13 * 3/√13)
⇒ (2 - 2)/(2 + 3)
⇒ 0
The value of the expression is 0.
Last updated on Jul 17, 2025
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