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If a cos 2 3 α + b cos 4 α = 16 cos 2 α + 9 cos 2 α is a identity then, a=1, b=24 a=3, b=24 a=4, b=2 a=7, b=18 Can u pls show detailed solution to this.....

If a cos23α + b cos4 α = 16 cos 2α + 9 cos 2α is a identity then, 
  1. a=1, b=24
  2. a=3,  b=24
  3. a=4, b=2
  4. a=7, b=18
Can u pls show detailed solution to this.....

Grade:11

1 Answers

Aditya Gupta
2075 Points
2 years ago
since a cos23α + b cos4 α = 16 cos 2α + 9 cos 2α = 25 cos 2α for all alpha, put alpha=0
so we have a+b=25 and a(cos^2α)(4cos^2α-3)^2+bcos^4α=25cos 2α so that a(4cos 2α -3)^2+bcos 2α=25 put α= 30 degree and we get a*0+b*3/4=25 so b=100/3
NOTE: the above question has some mistake because a cos23α + b cos4 α = 16 cos 2α + 9 cos 2α cannot be an identity, because the RHS of the equation is 16 cos 2α + 9 cos 2α which is equal to 25cos^2α , hence there is some misspelling. however, the basic method of solving such questions is given above 

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