If $y = \frac{sin x - cos x}{sin x + cos x}$ $y=(sinx-cosx)/(sinx+cosx)$ , then find the value of $1 + y^{2}$ $1+y^2$ ?

Question

If $y = \frac{sin x - cos x}{sin x + cos x}$ $y=(sinx-cosx)/(sinx+cosx)$ , then find the value of $1 + y^{2}$ $1+y^2$ ?

1 Answer

Related questions

What does it mean to prove a trigonometric identity?
How do you prove $csc θ \times tan θ = sec θ$ $\csc \theta \times \tan \theta = \sec \theta$ ?
How do you prove $(1 - {cos}^{2} x) (1 + {cot}^{2} x) = 1$ $(1-\cos^2 x)(1+\cot^2 x) = 1$ ?
How do you show that $2 sin x cos x = sin 2 x$ $2 \sin x \cos x = \sin 2x$ ? is true for $\frac{5 π}{6}$ $(5pi)/6$ ?
How do you prove that $sec x cot x = csc x$ $sec xcot x = csc x$ ?
How do you prove that $cos 2 x (1 + tan 2 x) = 1$ $cos 2x(1 + tan 2x) = 1$ ?
How do you prove that $\frac{2 sin x}{sec x (cos 4 x - sin 4 x)} = tan 2 x$ $(2sinx)/[secx(cos4x-sin4x)]=tan2x$ ?
How do you verify the identity: $- cot x = \frac{sin 3 x + sin x}{cos 3 x - cos x}$ $-cotx =(sin3x+sinx)/(cos3x-cosx)$ ?
How do you prove that $\frac{tan x + cos x}{1 + sin x} = sec x$ $(tanx+cosx)/(1+sinx)=secx$ ?
How do you prove the identity $\frac{sin x - cos x}{sin x + cos x} = \frac{2 {sin}^{2} x - 1}{1 + 2 sin x cos x}$ $(sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)$ ?

Impact of this question

2024 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-13T04:39:40

$1 + y^{2} = \frac{2}{1 + sin 2 x}$ $1+y^2=2/(1+sin2x)$

Explanation:

As $y = \frac{sin x - cos x}{sin x + cos x}$ $y=(sinx-cosx)/(sinx+cosx)$

$1 + y^{2} = 1 + {(\frac{sin x - cos x}{sin x + cos x})}^{2}$ $1+y^2=1+((sinx-cosx)/(sinx+cosx))^2$

$= \frac{{(sin x + cos x)}^{2} + {(sin x - cos x)}^{2}}{{((sin x + cos x))}^{2}}$ $=((sinx+cosx)^2+(sinx-cosx)^2)/((sinx+cosx))^2$

$= \frac{2 {sin}^{2} x + 2 {cos}^{2} x}{{sin}^{2} x + {cos}^{2} x + 2 sin x cos x}$ $=(2sin^2x+2cos^2x)/(sin^2x+cos^2x+2sinxcosx)$

$= \frac{2}{1 + sin 2 x}$ $=2/(1+sin2x)$

Science

Math

Humanities

... and beyond

If $y = \frac{sin x - cos x}{sin x + cos x}$ $y=(sinx-cosx)/(sinx+cosx)$ , then find the value of $1 + y^{2}$ $1+y^2$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

If y=(sinx-cosx)/(sinx+cosx)y=sinx−cosxsinx+cosxy=(sinx-cosx)/(sinx+cosx), then find the value of 1+y^21+y21+y^2?

1 Answer

Explanation:

Related questions

Impact of this question

If $y = \frac{sin x - cos x}{sin x + cos x}$ $y=(sinx-cosx)/(sinx+cosx)$ , then find the value of $1 + y^{2}$ $1+y^2$ ?