If Cosinex = 4/5 and x has its terminal side in quadrant lV, find the exact value of tangent 2x

Answer 1

Ifcosx = 4/5, then sinx = -3/5 in IV by Pythagoras.

tan 2x = sin 2x/cos 2x
= 2sinxcosx/(cos^2x - sin^2x)
= 2(-3/5)(4/5)/(16/25 - 9/25)
= (-24/25)/(7/25)
= (-24/25)(25/7) = -24/7