If \sin \theta-\cos \theta \leq \mu (\cos \theta+\sin \theta), then

treetopssan

treetopssan

Answered question

2022-01-24

If sinθcosθμ(cosθ+sinθ), then tanθ1+μ1μ

Answer & Explanation

spelkw

spelkw

Beginner2022-01-25Added 12 answers

If you divide both sides of the first inequality by cosθ, you obtain:
sinθcosθcosθ=tanθ1
μ(cosθ+sinθ)cosθ=μ(1+tanθ)
So, assuming cosθ>0, from the first inequality you obtain:
tanθ1μ(1+tanθ)(1μ)tanθ1+μ
Then, assuming 1μ>0, you obtain:
tanθ1+μ1μ
If cosθ<0, then by dividing both sides of the first inequality by cosθ, you must flip the sign. Therefore, the final inequality will be true provided that 1μ<0 holds instead.
euromillionsna

euromillionsna

Beginner2022-01-26Added 16 answers

μsinθcosθsinθ+cosθ
1+μ2sinθsinθ+cosθ
1μ2cosθsinθ+cosθ
1+μ1μtanθ

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