Question

If 4 tan teta=3,then
$(4 \sin(teta) - \cos(teta) \\ 4 \sin(teta ) + \cos(teta) is$
Please solve this problem step by step the first person to answer my question will be marked as brainliest answer fast please ​

Answer 1

Answer:

48/25

Step-by-step explanation:

4 tan theta = 3

tan theta = 3 / 4

tan theta =perpendicular / base

therefore , perpendicular = 3x

and base = 4x

Now ,

Hypotenuse ² = Perpendicular ² + Base ²

(Pythagoras theorem)

H² = (3x)² + (4x)²

H² = 9x²+16x²

H²= 25x²

H=✓25x²=5x

Now,

sin theta = Perpendicular /hypotenuse

= 3x/ 5x= 3/ 5

cos theta = Base / hypotenuse

= 4x/ 5x=4/5

Finally , $(4 \sin(teta) - \cos(teta) \\ 4 \sin(teta ) + \cos(teta)$

=(4× 3/ 5 -4/5)(4× 3/5 +4/5)

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

= (8/5)(16/5)

= 48/25