If θ be positive acute angle and 5cosθ + 12sinθ = 13, then the value of cosθ is

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

=> $$12sin\theta=13-5cos\theta$$

Squaring both sides,

=> $$(12sin\theta)^2=(13-5cos\theta)^2$$

=> $$144sin^2\theta = 169+25cos^2\theta-130cos\theta$$

=> $$144(1-cos^2\theta)=169+25cos^2\theta-130cos\theta$$

=> $$144-144cos^2\theta=169+25cos^2\theta-130cos\theta$$

=> $$169cos^2\theta-130cos\theta+25=0$$

=> $$(13cos\theta-5)^2=0$$

=> $$13cos\theta=5$$

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

=> Ans - (B)