Question

2.
(4 sin 0 - cos 0+1
If 4 tan 0 = 3, evaluate
( 4 sin 0 + cos 0-1)​

Answer 1

Given :-

4tan∅ = 3

➡ tan∅ = 3/4

We know that,

sin∅ = perpendicular/hypotenuse

cos∅ = base/hypotenuse

Consider any right angle triangle ABC right angle at B.

➡ tan∅ = BC/AB

➡ BC = 3k and AB = 4k

In ∆ABC, by using Pythagoras theorem, we get

➡ AC² = AB² + BC²

➡ AC² = (4k)² + (3k)²

➡ AC = √(16k² + 9k²)

➡ AC = √25k²

➡ AC = 5k

Now,

sin∅ = BC/AC = 3k/5k = 3/5

cos∅ = AB/AC = 4k/5k = 4/5

Hence, the value of 4 sin∅ + cos∅ - 1 :-

= (4 × 3/5) + 4/5 - 1

= 12/5 + 4/5 - 5/5

= (12 + 4 - 5)/5

= 11/5 FINAL ANSWER