Question
If sec a + tan a = 2, find the value of sin a.
Solution
Given, sec a + tan a = 2 ..............(I) We know that, sec² a - tan² a = 1 Or, (sec a + tan a) (sec a - tan a) = 1 So, sec a - tan a = (1/2) ...........(II) On adding equations (I) and (II), we get; 2 sec a = 2 + (1/2) = (5/2) Or, sec a = (5/4) So, cos a = [1/(sec a)] = (4/5) So, sin a = √[1 - (4/5)²] = √(9/25) = (3/5) Hence, sin a = (3/5)
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