Question

If 5 tan β = 4, then `(5  sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.

पर्याय

• `1/3`

• `2/5`

• `3/5`

• 6

Answer 1

If 5 tan β = 4, then `(5  sin β - 2 cos β)/(5 sin β + 2 cos β)` = `underline(bb(1/3)`.

Explanation:

Given, 5 tan β = 4

tan β = `4/5`

Now, `(5  sin β - 2 cos β)/(5 sin β + 2 cos β)`

Dividing numerator and denominator by cos β

= `(5  sin β/cos β - 2  cos β/cos β)/(5  sin β/cos β + 2  cos β/cos β)`

= `(5 tan β - 2)/(5 tan β + 2)`

Putting tan θ = `4/5`

= `(5 xx 4/5 - 2)/(5 xx 4/5 + 2)`

= `(4 - 2)/(4 + 2)`

= `2/6`

= `1/3`