Question

if cos theta is equals to 12 by 13 find the value of sin theta and tan theta also find the value of 2 sin minus tan theta where theta is e is acute angle ​

Answer 1

SOLUTION.

TRIGONOMETRY

You are now entered the world of amazes in which you can explore some of the basic properties of triangle through which you can relate the sides and the angles of the triangle this new world is a special branch of mathematics namely TRIGONOMETRY.

$\cos \alpha = \frac{base}{hypotan.} \\ acc \: to \: question \: \\ \cos \alpha = \frac{12}{13} \\ \\ by \: comparison \: we \: get \: \\ base(y) = 12units \\ hypotan \: (x)= 13units \\ \\ acc \: to \: pythagoras \\ \\ {(perpendicular)}^{2} + {(base)}^{2} = {(hypo)}^{2} \\ \\ {(perpendicular)}^{2} + 144 = 169 \\ {(perpendicular)}^{2} = 25 \\ perpendicular = 5units \\ \\ \sin \alpha = \frac{perpendicular}{hypo} \\ \\ \sin \alpha = \frac{5}{13} \\ \\ \tan \alpha = \frac{perpendicular}{base} \\ \\ \tan \alpha = \frac{5}{12} \\ \\ 2 \sin \alpha - \tan \alpha = 2( \frac{5}{13} ) - \frac{5}{12} \\ \\ 2 \sin \alpha - \tan \alpha = 5( \frac{2}{13} - \frac{1}{12} ) \\ \\ take \: lcm \\ \\ 2 \sin \alpha - \tan \alpha = 5( \frac{24 - 13}{156} ) \\ \\ 2 \sin \alpha - \tan \alpha = \frac{5 \times 11}{156} \\ \\ 2 \sin \alpha - \tan \alpha = \frac{55}{156}$