Question

if 2sinx+cosx=1,then 7cosx 6sinx is equal to


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Answer 1

Answer:

Step-by-step explanation:

2sinx + cosx = 1------------>(i)

⇒2sinx = 1 - cosx

⇒3*(2sinx) = 2*(1 - cosx) (Multiplying both sides by 2)

⇒6sinx = 2 - 2cosx--------->(ii)

Also,

2sinx + cosx = 1

cosx = 1 - 2sinx

⇒7*(cosx) = 7*(1 - 2sinx)

⇒7cosx = 7 - 14sinx------------>(iii)

∴7cosx 6sinx = (ii) * (iii)

                      = (7 - 14sinx)(2 - 2cosx)

                      =7(2 - 2cosx) - 14sinx(2 - 2cosx)

                      =14 - 14cosx - (28sinx - 28sinxcosx)

                      =14 - 14cosx - 28sinx + (14 * 2sinxcosx)

                      =14 - 14(cosx + 2sinx) + 14sin2x              (∵2sinxcosx = sin2x)

                      =14 -14*(1) + 14sin2x      (from (i), ie the question.)

                      =0 + 14sin2x   =   14sin2x