Question

How do you simplify `f(theta)=sin4theta-2cot2theta+5csc2theta` to trigonometric functions of a unit `theta`?

Answer 1

Transform trig expression

Explanation:

Use the 2 trig identities:
sin 2a = 2sin a.cos a
`cos 2a = 2cos^2 a - 1`
a. sin 4t = 2sin 2t.cos 2t =
b. `- 2cot 2t = - 2(cos 2t)/(sin 2t)`
`a + b = 2cos 2t(sin 2t)/(-sin 2t) = - 2cos 2t = -2(2cos^2 t - 1)`
`c = 5csc 2t = 5/(sin 2t) = 5/(2sin t.cos t)`
Finally:
`f(t) = a + b + c = -2(2cos^2 t - 1) + 5/(2sin t.cos t)`