Question:
Find the simplified form of cos-1 [3/5 cos x + 4/5 sin x], x ∈ [-3π/4, π/4].
Solution:
We have,
cos-1 [3/5 cos x + 4/5 sin x], x ∈ [-3π/4, π/4]
Now, let cos α = 3/5
So, sin α = 4/5 and tan α = 4/3
cos-1 [3/5 cos x + 4/5 sin x]
⇒ cos-1 [3/5 cos x + 4/5 sin x] = cos-1 [cos α cos x + sin α sin x]
= cos-1 [cos (α – x)]
= α – x
= tan-1 4/3 – x