Question

Verify the following identity:
sec(x)-sin(x)tan(x) = cos(x)

Please include steps! :/ Thank you!

Answer 1

Use tan x = sin/cos x, add and multiply through, then use cos^ x + sin^2 x =1

Answer 2

tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x)
substitution on original expression gives (1/cos(x)) - (sin(x) * (sin(x)/cos(x))) = cos(x)
=> 1/cos(x) - sin²(x)/cos(x) = cos(x)
=> (1 - sin²(x))/cos(x) = cos(x)
=> 1 - sin²(x) = cos²(x)
sin²(x) + cos²(x) = 1 is an identity