Question

What basic trigonometric identity would you use to verify that (sin2x + cos2x)/cosx=secx

Answer 1

Explanation:

`\frac{ \ {sin}^(2) x + { \cos}^(2) x}{cos \: x} = sec \: x \\ \\ LHS \\ = \frac{ \ {sin}^(2) x + { \cos}^(2) x}{cos \: x} \\ \\ = ( 1)/(cos \: x) \:( \because \: \ {sin}^(2) x + { \cos}^(2) x = 1) \\ \\ = sec \: x \\ = RHS \\`

Answer 2

Explanation:

sin(2x) = 2 sin(x) cos(x) cos(2x) = cos2(x) – sin2(x) = 1 – 2 sin2(x) = 2 cos2(x) – 1. Now I am not sure if this is right but I remember another similar formula. Here is the correct formula cot x = cos x / sin x

2 ) ( sin² x + cos² x ) / cos x = sec x

1/cos x = sec x

sec x = sec x

cos² x + sin² x = 1