Question

5cos(theta)+12sin(theta)=13 then find tan(theta)

Answer 1

5cos(theta)+12sin(theta)=13
5/13 *cos(theta)+12/13 *sin(theta)=1
let alpha such that cos(alpha)=5/13 and sin(alpha)=12/13
cos(alpha)*cos(theta)+sin(alpha)*sin(theta)=1
cos(theta-alpha)=1
theta=alpha+2pi*n, n integer
tan(theta)=sin(theta)/cos(theta)=sin(alpha+2pi*n)/cos(alpha+2pi*n)=sin(alpha)/cos(alpha)=(12/13)/(5/13)=12/5=2.4
tan(theta)=2.4