# Answer to Question #21707 in Trigonometry for Deepak Kumar

Question #21707

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

Expert's answer

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

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

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