Question

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

Answer 1

$\color{red}\huge\underline\mathcal{♡Solution♡}$

3cos∅-4sin∅ = 2cos∅+sin∅

3cos∅-2cos∅ = sin∅+4sin∅

cos∅ = 5sin∅

Also,

we know that,

tan∅ = sin∅/cos∅

= sin∅/5sin∅

= 1/5

$\huge\boxed{tan\:theta\:=\:1:5}$

Answer 2

Given : 3cos∅-4sin∅ = 2cos∅+sin∅

To find : tan∅

Solution : 3cos∅-4sin∅ = 2cos∅+sin∅

3cos∅- 2cos∅= 4sin∅+sin∅

cos∅ = 5sin∅

______

Also,

tan∅ = sin∅/cos∅

= sin∅/5sin∅

= 1/5 ( Answer )