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Some Applications Of Trigonometry

Question

The value of x if tan 3x = (sin 45° . cos 45°) sin 30°:
14°
15°
16°
20°

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Solution

15°

tan 3 straight x space equals space open parentheses fraction numerator 1 over denominator square root of 2 end fraction cross times fraction numerator 1 over denominator square root of 2 end fraction close parentheses divided by 1 half equals 1 half cross times 2 over 1 equals 1 equals tan 45 degree comma space space 3 straight x space equals space 45 degree space space rightwards double arrow space straight x space equals space 15 degree