If {\tan\theta + \cot\theta}/ {\tan\theta - \cot\theta} = 2, (0 ≤ θ ≤ 90°), then the value of sin θ is

SSC CPO SI and ASI 2011 Paper

Question : 144 of 200

Marks: +1, -0

{tanθ + cotθ}/ {tanθ - cotθ}

= 2, (0 ≤ θ ≤ 90°), then the value of sin θ is

Solution:

(2)

{\tan \θ+\cot θ}/{\tan \θ-\cot \θ}=2

By Componendo and dividendo,

⇒\;\;{\tanθ+\cotθ+\tanθ-\cotθ}/{\tanθ+\cotθ-\tanθ+\cotθ}

{2+1}/{2-1}

⇒\;\;{2\tanθ}/{2\cotθ}=\;\;{3}/{1}

⇒\;\;{\sin^{2}θ}/{\cos^{2}θ}=\;\;{3}/{1}

⇒\sin^{2}θ=3(1-\sin^{2}θ)

\;\text"Therefore,"\;\sin^{2}θ=\;\;{3}/{4}⇒\sinθ=\;\;{√{3}}/{2}

Go to Question:

Prev Question

Next Question