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If 3sinx + 4cosx = 5, then 4sinx - 3cosx =....???

  1. 0

  2. -5

  3. 1/5

  4. 5

plz explain me in detail... how to do questions like this... 

3 years ago


Answers : (2)


ANS    3sinx+4cosx=5

     => 3/5 sinx +4/5 cosx = 1

     let cosA=3/5   => sinA=4/5

     =>  cosAsinx + sinAcosx = 1

     =>  sin(x+A) = 1


       4sinx - 3cosx

  =   5(4/5sinx - 3/5 cosx)     [multipying numerator and denominator by 5]

  =   5(sinAsinx - cosAcosx)

  =   -5{cos(x+A)} = -5[root{1-(sin(x+A)^2)}] = -5 x 0 = 0          Ans 0


TRICK: if asinx+bcosx is given then multiply numerator and denominator by root(a^2 +b^2)

            this method is useful  in many questions 



 PLEASE       APPROVE       MY       ANSWER       IF       YOU       LIKE       IT


3 years ago


Squaring on both sides.

(3sinx+4cosx) 2 = 25

9sin2x +16 cos2x+24sinxcosx=25

9(1- cos2x)+16(1- sin2x)+ 24sinxcosx=25

9-9 cos2x+16-16 sin2x+24sinxcosx=25

25-9 cos2x-16 sin2x+24sinxcosx=25

9 cos2x+16 sin2x-24sinxcosx=0

(3cosx-4sinx) 2 = 0



2 years ago

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