Question

49. Number of solution for equation 2 tan²x + sec²x=2 for 0≤x≤2π are​

Answer 1

Answer:

This can be written as:

2sin2xcos2x+1cos2x=2, using the identities tanθ=sinθcosθ and secθ=1cosθ

Simplifying:

2sin2x+1cos2x=2

2sin2x+1=2cos2x

Apply the identity sin2x+cos2x=1→sin2x=1−cos2x to the left-hand side.

2(1−cos2x)+1=2cos2x

2−2cos2x+1=2cos2x

3=4cos2x

34=cos2x

±√32=cosx

x=π6,5π6,7π6and11π6

Note that these solutions are only those that are in the interval 0≤x<2π.

Hopefully this helps!