Question
If sec a + tan a = 3, find the value of sin a.Ā
Solution
Given, sec a + tan a = 3 ..............(I)Ā We know that, secĀ² a - tanĀ² a = 1Ā Or, (sec a + tan a) (sec a - tan a) = 1Ā So, sec a - tan a = (1/3) ...........(II)Ā On adding equations (I) and (II), we get;Ā 2 sec a = 3 + (1/3) = (10/3)Ā Or, sec a = (5/3)Ā So, cos a = [1/(sec a)] = (3/5)Ā So, sin a = ā[1 - (3/5)Ā²] = ā(16/25) = (4/5)Ā Hence, sin a = (4/5)Ā
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