How do you prove that $\frac{cos x}{1 - sin x} - \frac{1}{cos x} = tan x$ $cosx/(1-sinx) - 1/cosx = tanx$ ?

Question

How do you prove that $\frac{cos x}{1 - sin x} - \frac{1}{cos x} = tan x$ $cosx/(1-sinx) - 1/cosx = tanx$ ?

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

24037 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-16T16:06:36

$f (x) = \frac{cos x}{1 - sin x} - \frac{1}{cos x} = \frac{{cos}^{2} x - (1 - sin x)}{cos x \cdot (1 - sin x)}$ $f(x) = cos x/(1 - sin x) - 1/cos x = [cos ^2 x - (1 - sin x)]/(cos x*(1 - sin x)$

In the numerator of $f (x),$ $f(x),$ replace

${cos}^{2} x = 1 - {sin}^{2} x$ $cos^2 x = 1 - sin^2 x$

Numerator $= 1 - {sin}^{2} x - 1 + sin x =$ $= 1 - sin^2 x - 1 + sin x =$

$sin x \cdot (1 - sin x)$ $sin x*(1 - sin x)$

$f (x) = \frac{sin x \cdot (1 - sin x)}{cos x \cdot (1 - sin x)} = \frac{sin x}{cos x} = tan x .$ $f(x) = (sin x*(1 - sin x))/(cos x*(1 - sin x))= sin x/cos x = tan x.$

Science

Math

Humanities

... and beyond

How do you prove that $\frac{cos x}{1 - sin x} - \frac{1}{cos x} = tan x$ $cosx/(1-sinx) - 1/cosx = tanx$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you prove that cosx/(1-sinx) - 1/cosx = tanxcosx1−sinx−1cosx=tanxcosx/(1-sinx) - 1/cosx = tanx?

1 Answer

Related questions

Impact of this question

How do you prove that $\frac{cos x}{1 - sin x} - \frac{1}{cos x} = tan x$ $cosx/(1-sinx) - 1/cosx = tanx$ ?