How do you verify the identify sinθtanθ+cosθ=secθ?
3 Answers
Mar 9, 2018
See the proof below
Explanation:
We need
Therefore,
Mar 9, 2018
Apply the identities
Explanation:
Apply the identity
Apply the Pythagorean theorem
By the definition of secants
Mar 9, 2018
Explanation:
using the trigonometric identities
∙xtanθ=sinθcosθ and secθ=1cosθ
∙xsin2θ+cos2θ=1
Consider the left side
⇒sinθtanθ+cosθ
=sinθ×sinθcosθ+cosθ
=sin2θcosθ+cos2θcosθ←common denominator cosθ
=sin2θ+cos2θcosθ
=1cosθ=secθ= right side ⇒ verified