If (1 – cosP)(1 + cosP) = $$\frac{3}{4}$$​ and P is an acute angle, then find the value of secP.

Correct option is C

Given:

The equation $$(1 - \cos P)(1 + \cos P) = \frac{3}{4}$$​​

Formula Used:

​$$\sin^2 P + \cos^2 P = 1$$​

​$$\sec P = \frac{1}{\cos P}$$​​

Solution:

​$$(1 - \cos P)(1 + \cos P) = 1 - \cos^2 P =\sin^2 P = \frac{3}{4}$$​​

Since P is an acute angle, sin P is positive:

​$$\sin P = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}$$ 

P = 60$$\degree$$​​

​$$\cos P=\cos 60° = \frac{1}{2}$$​​

Since P is an acute angle, cos P is positive.

​$$\sec P = \frac{1}{\cos P} = \frac{1}{\frac{1}{2}} = 2$$