Is the expression true: (cos(-theta))/(1+sin(-theta))=sectheta+tantheta

Jaden Easton

Jaden Easton

Answered question

2020-10-19

Is the expression true:
cos(θ)1+sin(θ)=secθ+tanθ

Answer & Explanation

Anonym

Anonym

Skilled2020-10-20Added 108 answers

cos(θ)1+sin(θ)=secθ+tanθ
To identify, use:
sin(x)=sin(x)
cos(x)=cos(x)
cos(θ)1+sin(θ)=cos(θ)1sin(θ)
Use the rules:
ab=(ab)(a+b)a+b=a2b2a+b
and
1sin(x)=1sin2(x)1+sin(x)
cos(θ)1sin(θ)=cos(θ)cos2(θ)1+sin(θ)
=1+sin(θ)cos(θ)
R.H.S.
sec(θ)+tan(θ)=1cos(θ)+sin(θ)cos(θ)=1+sin(θ)cos(θ)
Thus L.H.S.=R.H.S. and the expressin is true

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