If θ is an acute angle and cotθ = $$\frac{12}{35}$$​, what is the value of secθ?

Correct option is B

Given:

​$$\cot \theta = \frac{12}{35}$$​​

θ is an acute angle.

Formula Used:

​$$\cot \theta = \frac{\cos \theta}{\sin \theta}$$​​

​$$\sin^2 \theta + \cos^2 \theta = 1$$​

​$$\sec \theta = \frac{1}{\cos \theta}$$​​

Solution:

​$$\frac{\cos \theta}{\sin \theta} = \frac{12}{35}$$​​

Therefore, let $$\cos \theta$$​= 12k and $$\sin \theta =$$​35k for some constant k.

​$$\sin^2 \theta + \cos^2 \theta = 1$$​
​$$(35k)^2 + (12k)^2 = 1$$​​

​$$1225k^2 + 144k^2 = 1$$​​

​$$1369k^2 = 1$$​​

​$$k^2 = \frac{1}{1369}$$​​

​$$k = \frac{1}{37}$$​

$$\cos \theta = 12k = 12 \times \frac{1}{37} = \frac{12}{37}$$​

​$$\sec \theta = \frac{1}{\cos \theta} = \frac{1}{\frac{12}{37}} = \frac{37}{12}$$​