Question

tan theta is 5/12 , 1 + sin a 1. If tan e If tan 0 =--. then find the value of 5 1 - sin e​

Answer 1

Answer:

$\rm 25$

Step-by-step explanation:

We have,

$\tan θ = \dfrac{12}{5}$

$\tan ^2 θ = \dfrac{144}{25}$

$\tan ^2 θ +1 = \dfrac{144}{25} +1$

$\sec ^2 θ = \dfrac{144+25}{25}$

$\sec ^2 θ = \dfrac{169}{25}$

$\sec θ = \sqrt{\dfrac{169}{25} }$

$\sec θ = \dfrac{13}{5}$

$\cos θ = \dfrac{5}{13}$

$\cos ^2 θ = \dfrac{25}{169}$

$1- \cos ^2 θ = 1- \dfrac{25}{169}$

$1- \cos ^2 θ = \dfrac{169-25}{169}$

$1- \cos ^2 θ = \dfrac{144}{169}$

$\sin ^2 θ = \dfrac{144}{169}$

$\sin θ = \sqrt{\dfrac{144}{169}}$

$\sin θ = \dfrac{12}{13}$

$\dfrac{1+\sin θ}{1- \sin θ} = \dfrac{1+ \frac{12}{13}}{1-\frac{12}{13}}$

$\implies \dfrac{ \dfrac{13+12}{13}}{\dfrac{13-12}{13}}$

$\implies \dfrac{ 13+12}{13-12}$

$\implies \dfrac{ 25}{1}$

$: \implies 25$