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find the general solution of the eqquation 4cos(x) +3 Sin (x)=5

find the general solution of the eqquation  4cos(x) +3 Sin (x)=5
 

Grade:11

1 Answers

Y RAJYALAKSHMI
45 Points
9 years ago
4(1 – 2sin2x/2) + 3(2sinx/2* cosx/2) – 5 = 0
4 – 8 sin2x/2 + 6sinx/2 cosx/2 – 5 = 0 
– 8 sin2x/2 + 6sinx/2 cosx/2 – 1 = 0 
– 8 sin2x/2 + 6sinx/2 cosx/2 – (sin2x/2 + cos2x/2) = 0 
– 9 sin2x/2 + 6sinx/2 cosx/2 – cos2x/2 = 0 
(3 sinx/2 – cosx/2)2 = 0
3 sinx/2 – cosx/2 = 0 =>  3 sinx/2 =  cosx/2 => 3 (sinx/2) / (cosx/2) = 1 => 3 tan x/2 = 1
=> tanx/2 = 1/3 
=> x/2 = tan –1 1/3 
Gen Solution x/2 = nπ + tan –1 1/3  = > x = 2nπ + 2tan –1 1/3
 
Ans: x = 2nπ + 2tan –1 1/3
 
 
 
 

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