Question

If cos a=3/5,then find the value of sin a-cos a/2tan a

Answer 1

cos a = 3/5 = ab/a.c.
$ab \: = 3 \\ ac = 5 \\ by \: phythgorus \: theorem \\ ac {}^{2} = ab {}^{2} + bc {}^{2} \\ 5 {}^{2} = 3 {}^{2} + bc {}^{2} \\ 25 = 9 + bc {}^{2} \\ bc {}^{2} = 25 - 9 = 8 \\ bc = \sqrt{8} \\ bc = 2 \sqrt{2} \\ \sin(a) \: \: = \frac{bc}{ac} \\ = \frac{2 \sqrt{2} }{5}$
$\tan(a) = \frac{ \sin(a) }{ \cos(a) } = \frac{ \sqrt{2} }{5} \times \frac{5}{3} = \frac{ \sqrt{2} }{3}$
$\sin(a) - \frac{ \cos(a) }{2 \tan(a) } = \frac{2 \sqrt{2} }{5} - \frac{3}{5} \times \frac{3}{ \sqrt{2} } = \frac{2 \sqrt{2} }{5} - \frac{6}{5 \sqrt{2 } } = \frac{20}{25 \sqrt{2} } - \frac{30}{25 \sqrt{2} } = \frac{ - 10}{25 \sqrt{2} } = \frac{ - 2}{5 \sqrt{2} }$