Question

if tan a = 4/3.evaluate sin a +cos a /sin a -cos a

Answer 1

tan=4/3
sin =4/5
cos=3/5
sina +cosa=7/5
sina-cosa=1/5
sins+cosa/sina-cosa=7

Answer 2

tan a=4/3 = p/b ( Here, p= perpendicular and b= base)

By Pythagoras theorem,

H²= p² + b²

h= √16+9 = 5

Now, sin a= p/h = 4/5 ; cos a = b/h = 3/5

So, sin a + cos a ⇒ 4/5 + 3/5 = 7/5

sin a - cos a ⇒ 4/7-3/7 = 1/7

sin a + cos a / sin a -cos a = (7/5) / (1/5) = 7/5 × 5/1 = 7