How do you prove $sec x - cos x = sin x tan x$ $sec x - cos x = sin x tan x$ ?

Question

How do you prove $sec x - cos x = sin x tan x$ $sec x - cos x = sin x tan x$ ?

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

18082 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-13T21:41:50

See explanation...

Explanation:

$sec (x) = \frac{1}{cos (x)}$ $sec(x) = 1/cos(x)$

$tan (x) = \frac{sin (x)}{cos (x)}$ $tan(x) = sin(x)/cos(x)$

${sin}^{2} (x) + {cos}^{2} (x) = 1$ $sin^2(x) + cos^2(x) = 1$

So:

$sec (x) - cos (x)$ $sec(x) - cos(x)$

$= \frac{1}{cos (x)} - cos (x)$ $= 1/(cos(x)) - cos(x)$

$= \frac{1}{cos (x)} - \frac{{cos}^{2} (x)}{cos (x)}$ $=1/(cos(x)) - cos^2(x)/cos(x)$

$= \frac{1 - {cos}^{2} (x)}{cos (x)}$ $=(1-cos^2(x))/cos(x)$

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

$= sin (x) \frac{sin (x)}{cos (x)}$ $=sin(x)sin(x)/cos(x)$

$= sin (x) tan (x)$ $=sin(x)tan(x)$

Science

Math

Humanities

... and beyond

How do you prove $sec x - cos x = sin x tan x$ $sec x - cos x = sin x tan x$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you prove sec x - cos x = sin x tan xsecx−cosx=sinxtanxsec x - cos x = sin x tan x?

1 Answer

Explanation:

Related questions

Impact of this question

How do you prove $sec x - cos x = sin x tan x$ $sec x - cos x = sin x tan x$ ?