Question

if tan theta =3tan theta-4 find the value of 4cos theta - sin theta by 2 cos theta +sin theta

Answer 1

Answer:

1/2

Step-by-step explanation:

Here tanФ = 3tanФ -4

2tanФ = 4

tanФ = 2 --- ( i )

Now

$\frac{4cos\theta - sin \theta}{2 cos \theta + sin \theta}$

Dividing Numerator and Denominator by cosФ

$\frac{4\frac{cos\theta}{cos\theta} - \frac{sin \theta}{cos\theta}}{2 \frac{cos \theta}{cos\theta} + \frac{sin \theta}{cos\theta}}$

[∵ sinФ/cosФ = tanФ]

$\frac{4 - tan\theta}{2 + tan\theta}$

Putting tanФ = 2 from eq( i )

$\frac{4-2}{2+2}$

= 2/4

= 1/2