if 13 sin tita =5 find the value of (5 sin tita -2 cos tita)by tan tita

Question

if 13 sin tita =5 find the value of (5 sin tita -2 cos tita)by
tan tita

Ajanta Trivedi · Accepted Answer

the given equation is : $13 \sin θ = 5 \Rightarrow \sin θ = \frac{5}{13}$

$\cos θ = \frac{\sqrt{13^{2} - 5^{2}}}{13} = \frac{\sqrt{169 - 25}}{13} = \frac{\sqrt{144}}{13} [f o r 0 < θ < 90] \cos θ = \frac{12}{13} \tan θ = \frac{\sin θ}{\cos θ} = \frac{5 / 13}{12 / 13} \tan θ = \frac{5}{12}$

therefore

$\frac{5 \sin θ - 2 \cos θ}{\tan θ} = \frac{5 * \frac{5}{13} - 2 * \frac{12}{13}}{5 / 12} = \frac{\frac{25}{13} - \frac{24}{13}}{5 / 12} = \frac{25 - 24}{13} * \frac{12}{5} = \frac{1}{13} * \frac{12}{5} = \frac{12}{65}$

hope this helps you.

cheers!!