Question
If sec a + tan a = 3/2, find the value of sin a.Â
Solution
Given, sec a + tan a = (3/2) ..............(I)  We know that, sec² a - tan² a = 1  Or, (sec a + tan a) (sec a - tan a) = 1  So, sec a - tan a = (2/3) ...........(II)  On adding equations (I) and (II), we get;  2 sec a = (3/2) + (2/3) = (9 + 4)/6 = (13/6) Or, sec a = (13/12)  So, cos a = [1/(sec a)] = (12/13)  So, sin a = √[1 - (12/13)²] = √(25/169) = (5/13)  Hence, sin a = (5/13)
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