Question #49284

Question

Question #49284

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

1578 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-17T18:10:24

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

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

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

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

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

$= cos x$ $=cosx$

Science

Math

Humanities

... and beyond

Question #49284

1 Answer

Related questions

Impact of this question