Question

If tan ⁡x=12/5, and 0°

Answer 1

The value of sin(2x) is
`(120)/(169)`

Step-by-step explanation:

Given that
`tan x =(12)/(5)`

The formula for
`sin(2x)` is
`\sin (2 x)=2 \sin x \cos x`

Since,
`\tan x=(o p p)/(a d j)`

Also, it is given that
`tan x =(12)/(5)`

Thus,
`opp=12` and
`adj=5`

To find the hypotenuse, let us use the pythagoras theorem,

`\begin{aligned}h y p &=\sqrt{12^(2)+5^(2)} \\&=√(144+25) \\&=√(169) \\&=13\end{aligned}`

Now, we can find the value of sin x and cos x.

`\sin x=\frac{\text { opp }}{h y p}=(12)/(13)`

`\cos x=(a d j)/(h y p)=(5)/(13)`

Now, substituting these values in the formula for sin 2x, we get,

`\begin{aligned}\sin (2 x) &=2 \sin x \cos x \\&=2\left((12)/(13)\right)\left((5)/(13)\right) \\&=(120)/(169)\end{aligned}`

Thus, the value of sin(2x) is
`(120)/(169)`