Question

If sin ⁡x=725, and 0 ∠ x ∠ pi/2, what is the tan (x - pi/4)

∠ isn't the angle simple it is the less than but for some reason it wasn't letting me put that one in.

Enter your answer as a fraction in simplest form, like this: 3/14

Answer 1

`Tan(x-(\pi )/(4)) = (-17)/(31)`

Explanation:

Here we have , sin ⁡x=7/25( given sin x = 725 which is not possible ) ,
`0<x<(\pi )/(2)` . Let's find tan (x - pi/4):

⇒
`Tanx = (sinx)/(cosx)`

⇒
`Tanx = \frac{sinx}{\sqrt{1-(sinx)^(2)}}`

⇒
`Tanx = \frac{(7)/(25)}{\sqrt{1-((7)/(25))^(2)}}`

⇒
`Tanx = {(7)/(25)}{\sqrt{((625)/(625-49))^{}}}`

⇒
`Tanx = {(7)/(25)}((25)/(24) )`

⇒
`Tanx = {(7)/(24)}`

Now ,
`Tan(x-(\pi )/(4)) = (Tanx - Tan((\pi )/(4) ))/(1+ Tanx(Tan((\pi )/(4) ))`

⇒
`Tan(x-(\pi )/(4)) = (Tanx -1)/(1+ Tanx(1))`

⇒
`Tan(x-(\pi )/(4)) = ((7)/(24) -1)/(1+(7)/(24) )`

⇒
`Tan(x-(\pi )/(4)) = ((7-24)/(24) )/((7+24)/(24) )`

⇒
`Tan(x-(\pi )/(4)) = (-17)/(24) ((24)/(31) )`

⇒
`Tan(x-(\pi )/(4)) = (-17)/(31)`