Friday, 8 March 2019

trigonometry - Trig Identity Proof frac1+sinthetacostheta+fraccostheta1sintheta=2tanleft(fractheta2+fracpi4right)



I've been working on this for like half an hour now and don't seem to be getting anywhere. I've tried using the double angle identity to write the LHS with θ/2 and have tried expanding the RHS as a sum. The main issue I'm having is working out how to get a π on the LHS or removing it from the right to equate the two sides.
1+sinθcosθ+cosθ1sinθ=2tan(θ2+π4)


Answer



hint:

cosθ=cos2(θ/2)sin2(θ/2)=(cos(θ/2)+sin(θ/2))(cos(θ/2)sin(θ/2)),1±sinθ=(cos(θ/2)±sin(θ/2))2.


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