Question

if tan theta = 24/25 ,find without using tables or calculator the value of tan theta-cos theta/ cos theta + sin theta

Answer 1

tan theta = perpendicular/ base

tan theta = 24/25

perpendicular = 24, base = 25

By Pythagoras theorem,

(perpendicular)² + (base)² = (hypotenuse)²

24² + 25² = h²

h = √(24² + 25²)

h = 34.66

so, sin theta = 24/34.66

and, cos theta = 25/34.66

thus, [tan(theta) - cos(theta)] / [cos(theta) + sin(theta)]

(24/25 - 25/34.66) / (25/34.66 + 24/34.66)

0.2387/ 1.414

0.2093