Question

If tan A =3/4,then sinA cosA =12/15,prove it

Answer 1

Step-by-step explanation:

sin A cos A should be equal to $\frac{12}{25}$ and not $\frac{12}{15}$ as it is mentioned in the question.

Given:

$tan A = \frac{3}{4} \\ \because \: sec ^{2} A = 1 + tan ^{2} A \\ = 1 + ( \frac{3}{4} )^{2} \\ = 1 + \frac{9}{16} \\ = \frac{16 + 9}{16} \\ \implies \: sec ^{2} A = \frac{25}{16} \\ \implies \: sec A = \frac{5}{4} \\ \because \: cos A = \frac{1}{sec A } \\ \therefore \: cos A = \frac{1}{ \frac{5}{4} } \\ \implies cos A = \frac{4}{5} \\ now \: \\ sin A = tan A \times cos A \\ = \frac{3}{4} \times \frac{4}{5} \\ \implies \: sin A = \frac{3}{5} \\ sin A \: cos A = \frac{3}{5} \times \frac{4}{5} \\ sin A \: cos A = \frac{12}{25} \\ thus \: proved$