Question #cf9c7

Question

Question #cf9c7

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

1481 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-05T04:38:04

$sec (x) csc (x) - sec (- x) csc (- x) = 2 sec (x) csc (x)$ $sec(x)csc(x) - sec(-x)csc(-x)=2sec(x)csc(x)$

Explanation:

For this problem, we will make use of the facts that

- $csc (- x) = - csc (x)$ $csc(-x) = -csc(x)$
- $sec (- x) = sec (x)$ $sec(-x) = sec(x)$

(these are due to sine being an odd function and cosine being an even function, together with the definitions of the secant and cosecant functions)

$sec (x) csc (x) - sec (- x) csc (- x)$ $sec(x)csc(x) - sec(-x)csc(-x)$

$= sec (x) csc (x) - sec (x) (- csc (x))$ $= sec(x)csc(x)-sec(x)(-csc(x))$

$= sec (x) csc (x) + sec (x) csc (x)$ $=sec(x)csc(x)+sec(x)csc(x)$

$= 2 sec (x) csc (x)$ $=2sec(x)csc(x)$

Science

Math

Humanities

... and beyond

Question #cf9c7

1 Answer

Explanation:

Related questions

Impact of this question