Question
If sec a + tan a = 5/2, find the value of sin a.Â
Solution
Given, sec a + tan a = (5/2) ..............(I)  We know that, sec² a - tan² a = 1 Or, (sec a + tan a) (sec a - tan a) = 1  So, sec a - tan a = (2/5) ...........(II)  On adding equations (I) and (II), we get;  2 sec a = (5/2) + (2/5) = (25 + 4)/10 = (29/10)  Or, sec a = (29/20)  So, cos a = [1/(sec a)] = (20/29)  So, sin a = √[1 - (20/29)²] = √(441/841) = (21/29)  Hence, sin a = (21/29)
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