Question

If sin θ = 12/13, 0° < θ < 90°, find the value of: sin² θ- cos² θ /2 sin θ. cos θ x 1/tan² θ​

Answer 1

Answer:

$\frac{595}{3456}$

Step-by-step explanation:

Given,

$\sin(a) = \frac{12}{13}$

${13}^{2} = {12}^{2}$

$169 - 144 = 25$

$5$

$\cos(a) = \frac{5}{13}$

$\tan(a) = \frac{12}{5}$

$therefore.$

$\frac{( \frac{12}{13} {)}^{2} - ( \frac{5}{13} {)}^{2} }{2( \frac{12}{13}) - ( \frac{5}{13} )} \times \frac{1}{( \frac{12}{5} {)}^{2} }$

$\frac{ (\frac{144}{169}) - (\frac{25}{169} )}{2( \frac{12}{13} )( \frac{5}{13} )} \times \frac{25}{144}$

$\frac{ (\frac{144 - 25}{169} )}{( \frac{120}{169} )} \times \frac{25}{144}$

$\frac{119}{120} \times \frac{25}{144}$

$\frac{119}{24} \times \frac{5}{144}$

$\frac{595}{3456}$