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Grade 12th passDifferential Calculus

1. Which of the following is equivalent to u= -cost+√3 sint?
A)u=2cos(t+ 2Π/3). B)u=1/2 cos(t+ 2Π/3). C)u=2cos(t - 2Π/3). D) u=1/2 cos(t - 2Π/3)
2. Which of the following products of trigonometric function of differential frequency is equation to cosΠt + cos2Πt ?
A) 2cos(Π/2 t)sin(Π/2 t) b) 2cos(3Π/2 t)cos(Π/2 t)
C) 2cos(3Π/2 t)cos(3Π/2 t) d) 2sin(3Π/2 t)cos(Π/2 t)

Question image for 1. Which of the following is equivalent to u= -co
Profile image of sana
7 Years agoGrade 12th pass
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1 Answer

Profile image of Rajat
ApprovedApproved Tutor Answer7 Years ago
-cost+√3sint=2[(-1/2)(cost)+(√3/2)(Sint)]
=2(cos2π/3.cost+sin2π/3.sint)
=2cos(2π/3-t) = 2cos(t-2π/3)
CosA+cosB= 2cos(A+B)/2.cos(A-B)/2
So, cosπt+cos2πt = 2cos(3πt/2).cos(πt/2)
 
I hope this helps
With regards.