How do you prove $(sin x + cos x) (tan x + cot x) = sec x + csc x$ $(sinx+cosx)(Tanx+cotx)=secx+cscx$ ?

Question

How do you prove $(sin x + cos x) (tan x + cot x) = sec x + csc x$ $(sinx+cosx)(Tanx+cotx)=secx+cscx$ ?

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

34885 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-22T04:42:59

We have:

$(sin x + cos x) (\frac{sin x}{cos x} + \frac{cos x}{sin x}) = sec x + csc x$ $(sinx + cosx)(sinx/cosx + cosx/sinx) = secx +cscx$

$(sin x + cos x) (\frac{{sin}^{2} x + {cos}^{2} x}{sin x cos x}) = sec x + csc x$ $(sinx + cosx)((sin^2x + cos^2x)/(sinxcosx)) = secx + cscx$

$\frac{sin x + cos x}{sin x cos x} = sec x + csc x$ $(sinx +cosx)/(sinxcosx) = secx + cscx$

$\frac{sin x}{sin x cos x} + \frac{cos x}{sin x cos x} = sec x + csc x$ $sinx/(sinxcosx) + cosx/(sinxcosx) = secx + cscx$

$\frac{1}{cos x} + \frac{1}{sin x} = sec x + csc x$ $1/cosx + 1/sinx = secx + cscx$

$sec x + csc x = sec x + csc x$ $secx + cscx = secx + cscx$

$L H S = R H S$ $LHS = RHS$

Hopefully this helps!

Science

Math

Humanities

... and beyond

How do you prove $(sin x + cos x) (tan x + cot x) = sec x + csc x$ $(sinx+cosx)(Tanx+cotx)=secx+cscx$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you prove (sinx+cosx)(tanx+cotx)=secx+cscx(sinx+cosx)(Tanx+cotx)=secx+cscx?

1 Answer

Related questions

Impact of this question

How do you prove $(sin x + cos x) (tan x + cot x) = sec x + csc x$ $(sinx+cosx)(Tanx+cotx)=secx+cscx$ ?