Question

If cos (50 degrees) = a, express tan (130 degrees) in terms of a.

Answer 1

Answer: The tan 130° is expressed as $\dfrac{\sqrt{1-a^2}}{a}$

Step-by-step explanation:

Since we have given that

$\cos 50^\circ=a$

As we know that

cos (π - θ ) = -cos θ

so, cos(180-50)=-cos 130° = -a

so, sin 130° would become

$\sqrt{1-(-a)^2}\\\\=\sqrt{1-a^2}$

So, tan 130° is given by

$\dfrac{\sin 130^\circ}{\cos 130^\circ}\\\\=\dfrac{\sqrt{1-a^2}}{a}$

Hence, the tan 130° is expressed as $\dfrac{\sqrt{1-a^2}}{a}$