If cos θ=12/13 , then the value of (sin θ (1-tan θ))/(tan θ(1+cosec θ)) is:

If cos θ=12/13 , then the value of (sin θ (1-tan θ))/(tan…

If cos $\theta=\frac{12}{13}$ , then the value of $\frac{sin \theta (1-tan \theta)}{tan \theta(1+cosec \theta)}$ is:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. $\frac{35}{234}$

cos $\theta=\frac{12}{13}$ = B/H

P = $\sqrt{169-144} = 5$

$\frac{sin \theta (1-tan \theta)}{tan \theta(1+cosec \theta)}$ = (P/H(1 - B/H))/(B/H(1 + H/P))

= [5/13(1 - 5/12)]/[5/12(1 + 13/5)]

= (5/13 × 7/12)/(3/2) = 35/234.