The question given is, If \(\displaystyle{x}{\cos{{\left(\theta\right)}}}-{\sin{{\left(\theta\right)}}}={1}\) then find

Angela Harrell

Angela Harrell

Answered question

2022-04-09

The question given is,
If xcos(θ)sin(θ)=1 then find the value of x2+(1+x2)sinθ

Answer & Explanation

resacarno4u

resacarno4u

Beginner2022-04-10Added 12 answers

The case cosθ=0 gives us sin(θ)=1 and so
x2+(1+x2)sinθ=1
When cosθ0, we have xcosθsinθ=1x=1+sinθcosθ and so
x2=1+2sinθ+sin2θcos2θ, 1+x2=2+2sinθcos2θ
which implies
x2+(1+x2)sinθ
=1+2sinθ+sin2θ+(2sinθ+2sin2θ)cos2θ
=2(1+2sinθ+sin2θ)+sin2θ1cos2θ=1+2x2
This means your expression is in general not identically equal to any constant.

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