Further Trigonometry?

Question

Use the new identities to solve:

3 sec^2 x = 5 + tan x in the range -180 <= x <= 180

Cheers peeps =P

Answer 1

3 sec^2 (x) = 5 + tan(x)

trig identigy
1 + tan^2(x) = sec^2(x)

3 (1+ tan^2(x) ) = 5 + tan(x)

distribute
3 + 3tan^2(x) = 5 + tan(x)

set the equation equal to 0
3tan^2(x) - tan(x) - 2 = 0

let y tan tan(x)
3y^2 - y - 2 = 0

factor
3y^2 - 3y + 2y - 2 = 0

(3y^2 - 3y) + (2y - 2) = 0

3y (y - 1) + 2(y - 1) = 0

(3y + 2) (y - 1) = 0

y = -2/3 or 1

tan(x) = 1
x = 45 or -135

tan(x) = -2/3
x =~ -36.69 or 146.31

Answer 2

This may help :-)

See "Summary" {about halfway down}