Dear friends, Please read our latest blog post for an important announcement about the website. ❤, The Socratic Team

# How do you prove the identity (sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

5
Bdub Share
Mar 9, 2018

See Below

#### Explanation:

Use the Property : color(blue)(sin^2x+cos^2x=1

$L H S : \frac{\sin x - \cos x}{\sin x + \cos x}$

$= \frac{\sin x - \cos x}{\sin x + \cos x} \cdot \frac{\sin x + \cos x}{\sin x + \cos x}$-> multiply by conjugate

$= \frac{{\sin}^{2} x - {\cos}^{2} x}{{\sin}^{2} x + 2 \sin x \cos x + {\cos}^{2} x}$

$= \frac{{\sin}^{2} x - \left[1 - {\sin}^{2} x\right]}{\left[{\sin}^{2} x + {\cos}^{2} x\right] + 2 \sin x \cos x}$

$= \frac{{\sin}^{2} x - 1 + {\sin}^{2} x}{1 + 2 \sin x \cos x}$

$= \frac{2 {\sin}^{2} x - 1}{1 + 2 \sin x \cos x}$

$= R H S$

• An hour ago
• An hour ago
• An hour ago
• An hour ago
• 25 minutes ago
• 35 minutes ago
• 40 minutes ago
• An hour ago
• An hour ago
• An hour ago
• An hour ago
• An hour ago
• An hour ago
• An hour ago