Target Mathematics

2.23: Differentiation with secant and solving a trig equation

0606/21/O/N/17 — Question 12 · 10 marks

(i)
Differentiate (cos⁡x)−1(\cos x)^{-1} with respect to xx.
[2]
(ii)
Hence find dydx\dfrac{\mathrm{d}y}{\mathrm{d}x} given that y=tan⁡x+4(cos⁡x)−1y = \tan x + 4(\cos x)^{-1}.
[2]
(iii)
Using your answer to part (ii), find the values of xx in the range 0≤x≤2π0 \le x \le 2\pi such that dydx=4\dfrac{\mathrm{d}y}{\mathrm{d}x} = 4.
[6]