Question

If sina=1/2 and a and b are complementary angles, then find the value of sin(a-b)

Answer 1

Answer:

$sin \: a \: = \frac{1}{2} \\ \implies \: sin \: a \: = \: sin \: 30 \degree \\ \implies \: a \: = 30 \degree \: \\ \because \: a \: and \: b \: are \: complementary \: \\ angles \: \\ \therefore \: a + b = 90 \degree \\ \implies \: b \: = 90 \degree - a \: = 90 \degree - 30 \degree \: \\ \implies \: b \: = 60 \degree \: \\ \therefore \: sin \: (a - b) = sin \: (30 \degree -90 \degree ) \\ = sin \: ( - 60 \degree ) \\ = - sin \: 60 \degree \\ = - \frac{ \sqrt{3} }{2}$