Thursday, August 29, 2019

trigonometry - Trigonometric Identities: fracsin2theta1+costheta=1costheta


sin2θ1+cosθ=1cosθ


Right Side: 1cosθ either stays the same, or can be 11secθ



Left Side: =sin2θ1+cosθ=1cos2θ1+cosθ=(1cosθ)(1+cosθ)1+cosθ=1cosθ


Is this correct?


Answer



Perhaps slightly simpler and shorter (FYI, what you did is correct): sin2x1+cosx=1cosxsin2x=(1cosx)(1+cosx)sin2x=1cos2x And since the last equality is just the trigonometric Pytahgoras Theorem we're done.


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