Find the angle x such that 0 is less than or equal to x which is less that 2pi. cos(2x)= =2-2sin^2x

Question

Find the angle x such that 0 is less than or equal to x which is less that 2pi. cos(2x)= =2-2sin^2x

Answer 1

Hi Angela,

 

cos(2x) = cos²x - sin²x  -   double angle formula

cos(2x) = 2 - 2sin²x

 

=> cos²x - sin²x = 2 - 2sin²x

 

<=> cos²x - sin²x + [2sin2x] = 2 - sin²x + [2sin²x]  adding 2sin²x to both sides

<=> cos²x + sin²x = 2

=> x = empty set because cos²x + sin²x = 1 and not 2 - this is one of the trig identities, Pythagorean Identity 

 

I hope this helps