Question

1.Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two
decimal places.

6.Prove that tan y cos^2 y + sin^2y/sin y = cos y + sin y

10.Prove that 1+tanθ/1-tanθ = sec^2θ+2tanθ/1-tan^2θ

17.Prove that sin^2w-cos^2w/tan w sin w + cos w tan w = cos w-cot w cos w

23.Find a counterexample to shows that the equation sec a – cos a = sin a sec a is not an identity.

Answer 1

1.
Some students like to look at these types the following way:
let tanx = y, to get
y^2 + y - 1 = 0
by formula ...
y = (-1 ± √5)/2
so tanx = (-1 ± √5)/2
using your calculator ....
x = 31.72° or 211.72°

or tanx = (-1 - √5)/2
x = 121.72° or 301.72°

#6, 10, 17,
establish correct order of operation, by using brackets.

#23
just pick any angle you want and use your calculator
or pick a = 30°, (you should know the trig values for 30°)