Question

if theta is an positive acute angle and 5 cos theta + 12 sin theta = 13 then cos theta is

Answer 1

this is your answer..

Answer 2

Answer:

The value of cosθ is $\frac{5}{13}$.

Step-by-step explanation:

The given equation is

$5\cos \theta+12\sin \theta=13$

Divide both sides by 13.

$\frac{5}{13}\cos \theta+\frac{12}{13}\sin \theta=1$        .... (1)

According to the identity formula of trigonometry.

$\cos^2 \theta+\sin^2 \theta=1$                                   .... (2)

On comparing (1) and (2), we get

$\cos \theta=\frac{5}{13}$

$\sin \theta=\frac{12}{13}$

Therefore value of cosθ is $\frac{5}{13}$.