Answer: The tan 130° is expressed as [tex]\dfrac{\sqrt{1-a^2}}{a}[/tex]
Step-by-step explanation:
Since we have given that
[tex]\cos 50^\circ=a[/tex]
As we know that
cos (π - θ ) = -cos θ
so, cos(180-50)=-cos 130° = -a
so, sin 130° would become
[tex]\sqrt{1-(-a)^2}\\\\=\sqrt{1-a^2}[/tex]
So, tan 130° is given by
[tex]\dfrac{\sin 130^\circ}{\cos 130^\circ}\\\\=\dfrac{\sqrt{1-a^2}}{a}[/tex]
Hence, the tan 130° is expressed as [tex]\dfrac{\sqrt{1-a^2}}{a}[/tex]
