Question

If 3cos theta-4sin theta=2cos theta+sin theta, find tan theta

Answer 1

3 cos - 4sin = 2cos + sin
3 cos - 2 cos = 4sin + sin
cos = 5sin
sin/ cos = 1/5
tan = 1/5

Answer 2

The value of tan⁡θ for the given is $\bold{\frac{1}{5}}$,  

Given:

$3 \cos \theta-4 \sin \theta=2 \sin \theta+\sin \theta$

To find:

The value of tan⁡θ from the given question.

Solution :

With the help of Trigonometric formulas, As we know that, tan⁡θ is the ratio between the sin⁡θ and cos⁡θ.

Then, from the given:

$3 \cos \theta-4 \sin \theta=2 \cos \theta+\sin \theta$

By arranging the terms,

$3 \cos \theta-2 \cos \theta=4 \sin \theta+\sin \theta$

$1 \cos \theta=5 \sin \theta$

$1=5 \frac{\sin \theta}{\cos \theta}$

$\frac{1}{5}=\frac{\sin \theta}{\cos \theta}$

From the trigonometric formula,

As all we know that the ratio of sin and cos

will get tan,

so $\frac{\sin \theta}{\cos \theta}=\tan \theta$

Then the value of tan⁡θ is $\frac{1}{5}$

$\frac{1}{5}=\tan \theta$