Question

if 4 tan theta is equal to 3 evaluate

Answer 1

QUESTION :
If 4tanA=3 then evaluate 4sinA-cosA+1/ 4sinA+cosA-1
SOLUTION :
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...

Answer 2

Hey there! ☺☻☺
Complete question:
If 4 tan= 3, evaluate (4 sin- cos+1÷4 sin+ cos-1)

Given,
4 tan = 3
∴ tan = 3/4

As we know,
Tan  = Perpendicular / base
Tan  = 3/4
Now,
Hypotenuse = √3² + 4² = √9+16 = √25 = 5

Using this, we can find:
Sin = Perpendicular / Hypotenuse = 3/5
Cos = Base / Hypotenuse = 4/5

ATQ,
(4sin - cos + 1)/(4sin + cos - 1) 
= (4 × 3/5 - 4/5 + 1)/(4 × 3/5 + 4/5 - 1)   [putting values]
= (12 - 4 + 5)/(12 + 4 - 5) 
= 13/11

Hope It Helps You! ☺☻☺