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

$Tan(x-\frac{\pi }{4}) = \frac{-17}{31}$

Step-by-step explanation:

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

⇒ $Tanx = \frac{sinx}{cosx}$

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

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

⇒ $Tanx = {\frac{7}{25}}{\sqrt{(\frac{625}{625-49})^{}}}$

⇒ $Tanx = {\frac{7}{25}}(\frac{25}{24} )$

⇒ $Tanx = {\frac{7}{24}}$

Now , $Tan(x-\frac{\pi }{4}) = \frac{Tanx - Tan(\frac{\pi }{4} )}{1+ Tanx(Tan(\frac{\pi }{4} )}$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{Tanx -1}{1+ Tanx(1)}$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{\frac{7}{24} -1}{1+\frac{7}{24} }$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{\frac{7-24}{24} }{\frac{7+24}{24} }$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{-17}{24} (\frac{24}{31} )$

⇒ $Tan(x-\frac{\pi }{4}) = \frac{-17}{31}$