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If (sin^2) x+3cosx-2=0, then what will be the (cos^3) x+(sec^3) x=

If (sin^2) x+3cosx-2=0, then what will be the (cos^3) x+(sec^3) x=
 

Grade:11

1 Answers

Aditya Gupta
2081 Points
4 years ago
Dear Student
sin^2x = 1 – cos^2 x
now
1 – cos^2 x + 3 cos x – 2=0
cos^2 x- 3cos x +1 = 0
let cos x = t
then it will form a quadratic equation
t^2 – 3t + 1 = 0
divide by t to get
t+1/t= 3....(1)
we are asked to find (cos^3) x+(sec^3) x= t^3+1/t^3
cubing (1)
t^3+1/t^3+3t*1/t(t+1/t)= 27
or t^3+1/t^3+3(3)= 27
or t^3+1/t^3= 18
kindly approve :)

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