Question

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

Answer 1

Answer: The tan 130° is expressed as
`(√(1-a^2))/(a)`

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

`√(1-(-a)^2)\\\\=√(1-a^2)`

So, tan 130° is given by

`(\sin 130^\circ)/(\cos 130^\circ)\\\\=(√(1-a^2))/(a)`

Hence, the tan 130° is expressed as
`(√(1-a^2))/(a)`