Question

If 4 cos ø- 3 sin ø = 3, find the value of 3 cos ø+ 4 sin ø​

Answer 1

Answer:

13/11

Step-by-step explanation:

GIVEN:

4tanA=3

tanA = ¾ = P/B

In a ∆ ABC right angled at B.

Base (AB) = 4 , Perpendicular( BC) = 3

AC² = AB² + BC²

[By Pythagoras theorem]

AC² = 4² + 3²

AC² = 16 + 9 = 25

AC= √25 = 5

The trigonometric ratios of ∠A,

Base (AB)= 4, perpendicular (BC)= 3 , hypotenuse(AC) = 5

sin A = perpendicular /hypotenuse = BC /AC sin A = ⅗

Cos A = Base/hypotenuse = ⅘

4sinA-cosA+1/4sinA+cosA-1

= 4×3/5 - ⅘ +1 / 4×3/5 + ⅘ -1

= 12/5 - (4 - 5/5 ) / 12/5 + (4 -5/5)

= 12/5 +⅕ / 12/5 -⅕

= 13/5 / 11/5

= 13/5 × 5/11 = 13/11

4sinA-cosA+1/4sinA+cosA-1 = 13/11.

HOPE THIS WILL HELP YOU...