The discussion revolves around solving trigonometric equations involving sine, cosine, and tangent functions, specifically the equations 2sin(x) + 1 = tan(x) and sin(2x) + cos(x) - sin(x) = 0, within the domain 0 ≤ x < 2π.
There is an ongoing exploration of different methods to approach the equations, with some participants providing hints and others questioning the outcomes of their manipulations. Guidance has been offered regarding the potential for extraneous solutions when squaring equations, prompting participants to verify their solutions against the original equations.
Some participants indicate a lack of familiarity with certain trigonometric identities and formulas, suggesting that their current understanding may limit their ability to fully engage with the problem. There is also mention of recent completion of a unit on related topics, which may affect participants' confidence in applying new concepts.
rock.freak667 said:What is sin2x-sinx equal to?
(Hint: Sum to product formula)
Nope said:I haven't learn that yet...
Sin(a+b),cos(a+b)...
Sin2A=2sinAcosA, cos2A=cosx^2-sin^2...
and sinx^2+cosx^2=1 ...and other form
this is all i know
We just finished this unit today, i don't think i will learn that...
Can i square both side?
sin2x+cosx-sinx=0
(sin2x)^2=(sinx-cosx)^2
(sin2x)^2=sinx^2-2cosxsinx+cosx^2
(sin2x)^2=1-sin2x
sin2x^x+sin2x-1=0
and then use quadratic
rock.freak667 said:yes that will work as well
Mark44 said:What did you get when you solved this equation?
sin2x^x+sin2x-1=0