Question

if sin 0=5/13, find the value of tan 0+1/cose​

Answer 1

★ Correct question :-

If sinθ = $\sf\dfrac{5}{13}$ , then find the value of tanθ + $\sf tan\theta + \dfrac{1}{cosec\theta}$

$\rule{200}1.5$

★ Solution :-

Firstly finding the other of the ∆

$\bf{Pythagoras\;theorem}\to\rm Hypotenuse^2 = base^2+Height^2$

If sinθ = $\sf\dfrac{5}{13}$

Then,

• Hypotenuse of the ∆ = 13
• Height of the ∆ = 5

Now ,

$\rm \longrightarrow Hyp^2=Base^2+Height^2\\\\\rm\longrightarrow 13^2=Base^2+5^2\\\\\rm\longrightarrow 169 - 25 = Base^2\\\\\rm Base = \sqrt{144}\\\\\boxed{\bf{Base=12}}$

Now,

• tanθ = $\rm\dfrac{Opposite}{Adjacent} = \dfrac{5}{12}$

• $\bf \dfrac{1}{cosec\theta}$=sinθ=$\rm\dfrac{5}{13}$

Substituting we have ,

$\rm \longrightarrow tan\theta + sin\theta \\\\\rm\longrightarrow \dfrac{5}{12} + {5}{13}\\\\\rm\longrightarrow \dfrac{65+60}{156}=\dfrac{126}{156}\\\\\longrightarrow\boxed{\bf tan\theta+\dfrac{1}{cosec\theta}=\dfrac{125}{156}}$