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Hello. Help me please. Solve the equation: 3^(sin^2x) + 3^(cos^2x) = 4 And find the roots belonging to the gap: [-2pi; -pi/2] Thank you very much.

Hello. Help me please.
 Solve the equation: 3^(sin^2x) +  3^(cos^2x) = 4
And find the roots belonging to the gap: 
[-2pi; -pi/2]
Thank you very much.

Grade:11

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
let 3^cos2x = t
 
then
 
3/t + t= 4
 
t^2 – 4t + 3= 0
 
t = 3 or t = 1
 
hence cos^2 x = 1 or cos^2 x = 0
 
hence npi/2 points are the roots.
 
so in [pi/2 , – pi/2], roots are pi/2, 0 , – pi/2
 

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