How do you prove the identity $\frac{csc θ - 1}{cot θ} = \frac{cot θ}{csc θ + 1}$ $(csc theta - 1) / cot theta = cot theta / (csc theta + 1)$ ?

Question

How do you prove the identity $\frac{csc θ - 1}{cot θ} = \frac{cot θ}{csc θ + 1}$ $(csc theta - 1) / cot theta = cot theta / (csc theta + 1)$ ?

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

10683 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-19T10:15:16

${sin}^{2} A + {cos}^{2} A = 1$ $sin^2 A + cos^2 A = 1$
$1 + {cot}^{2} A = {csc}^{2} A$ $1 + cot^2 A = csc^2 A$

$\frac{csc θ - 1}{cot θ} = \frac{(csc θ - 1) (csc θ + 1)}{cot θ (csc θ + 1)} = \frac{{csc}^{2} θ - 1}{cot θ (csc θ + 1)} = \frac{cot θ}{csc θ + 1}$ $(csc theta - 1)/cot theta = ((csc theta - 1)(csc theta + 1))/(cot theta (csc theta + 1)) = (csc^2 theta - 1)/(cot theta (csc theta + 1)) = cot theta/(csc theta + 1)$

Science

Math

Humanities

... and beyond

How do you prove the identity $\frac{csc θ - 1}{cot θ} = \frac{cot θ}{csc θ + 1}$ $(csc theta - 1) / cot theta = cot theta / (csc theta + 1)$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you prove the identity cscθ−1cotθ=cotθcscθ+1(csc theta - 1) / cot theta = cot theta / (csc theta + 1)?

1 Answer

Related questions

Impact of this question

How do you prove the identity $\frac{csc θ - 1}{cot θ} = \frac{cot θ}{csc θ + 1}$ $(csc theta - 1) / cot theta = cot theta / (csc theta + 1)$ ?