Question

If 4Sinx=3cosx, find the value of:
a) cosec²-cot²x+4
b) sec x
c) sin x

Answer 1

Answer:

Step-by-step explanation:

Given that,

4sinx = 3cosx

⇒ sin x / cos x = 3 / 4

⇒tan x = 3 / 4 = AB/ BC

By using Pythagoras theorem,

AC² = AB² + BC²

⇒ AC² = 3² + 4²

⇒ AC² = 9 + 16

⇒AC² = 25

⇒ AC = √25

⇒ AC = 5

a) cosec² x - cot² x = (5/3)² - (4/3)² = (25/9) - (16/9) = (25 - 16 ) / 9 = 9/9 = 1.

b) sec x = 5/4

c) sin x = 3/5