Question

Show that the equation 3sinxtanx = 8 can be written as 3cox^2x + 8cosx - 3

Answer 1

using the trigonometric identities

tanx =
`(sinx)/(cosx)` and sin²x = 1 - cos²x

3sinxtanx = 8

( 3sin²x)/ cosx = 8 ( multiply both sides by cosx )

3( 1 - cos²x ) = 8cosx

3 - 3cos² = 8cosx ( subtract 3 - 3cos²x from both sides )

0 = 3cos²x + 8cosx - 3