Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you solve $sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) = - 1$ $Sin(x + pi/4) + Sin(x - pi/4) = -1$ ?

1 Answer

A. S. Adikesavan

Feb 19, 2016

Solutions in [0, 2 $π$ $pi$ ] are 5 $π$ $pi$ /4 and 7 $π$ $pi$ /4.

Explanation:

Use sin (A+B) + sin(A $-$ $-$ B) = 2 sin 2A sin 2B.
The equation reduces to sin x = $-$ $-$ 1/ $\sqrt{}$ $sqrt$ 2.

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

See all questions in Proving Identities

Impact of this question

1790 views around the world

You can reuse this answer
Creative Commons License