Gradient for trigonometric functions

[Eklav Rai]

A curve has the equation Y=2 tan2x - 7 tanx
Find:
(a) an expression for the gradient of the curve
(b) the X-coordinates of each of the stationary points of the curve.

[Open Intelligence]

If this is an O-Level question, then the question should be y = 2tan ²x - 7tanx

(i) dy/dx (tan²x) = 2 tanx sec²x

dy/dx = 4 tanx sec²x - 7sec²x

(ii) at stationary points, dy/dx = 0

therefore, sec²x(4tanx - 7) = 0

sec ² x = 0 (reject)

tanx = 7/4

x = tan ^-1 (7/4)
key angle = 1.05

x = 1.05, 4.19