(1-sinA+cosA)/(sinA+cosA-1)=(1+cosA)/sinA

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

(1-sinA+cosA)/(sinA+cosA-1)=(1+cosA)/sinA

Postby Guest » Tue Dec 22, 2015 4:13 am

Solve the trigonometric equation:
[tex]\frac{1-\sin A+\cos A}{\sin A+\cos A-1}= \frac{1+\cos A}{\sin A}[/tex]
Guest
 

Re: (1-sinA+cosA)/(sinA+cosA-1)=(1+cosA)/sinA

Postby Guest » Tue Dec 22, 2015 7:49 am

To save typing let [tex]s=\sin A[/tex] and [tex]c=\cos A[/tex]
[tex](1-s+c)s = s-s^2+sc+(-1+s^2+c^2)+(c-c) = s+c-1+sc+c^2-c +(s^2-s^2) = (s+c-1)(1+c)[/tex]
Since
[tex](1-s+c)s = (s+c-1)(1+c)[/tex]
we know that
[tex]\frac{1-s+c}{s+c-1} = \frac{1+c}{s}[/tex]
provided that [tex]s\ne 0[/tex], and [tex]s+c-1\ne 0[/tex] (which occur when [tex]A=\pi n[/tex] or [tex]\pi/2+2\pi n[/tex] for some integer [tex]n[/tex]).

Hope this helped,

R. Baber.
Guest
 

Re: (1-sinA+cosA)/(sinA+cosA-1)=(1+cosA)/sinA

Postby Guest » Tue Dec 22, 2015 3:40 pm

Thank you very much.
Guest
 


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