Question

If 4 tan O = 3, evaluate
( 4 sino - cos 0+1
4 sin 0 + cos 0 -1)

Answer 1

4 tan Θ = 3

tan Θ = 3/4

Let perpendicular be 3k and base be 4k.

Then hypotenuse = √(3k)²+(4k)² = √9k²+16k²=√25k²=5k

sin Θ = p/h = 3k/5k = 3/5

cos Θ = b/h = 4k/5k = 4/5

4 sin Θ - cos Θ + 1 = 4 x 3/5 - 4/5 +1 = 12/5 - 4/5 - 5/5 = 3/5

4 sin Θ + cos Θ -1 = 4 x 3/5 + 4/5 +1 = 12/5 + 4/5 - 5/5 = 11/5