Answer to Question #11789 in Trigonometry for tanya jaiswal

Question

if α+β = 90° find the maximum and minimum values of sinα.sinβ

Answer 1

sinα.sinβ = (cos(α-β) - cos(α+β)) / 2
If α+β = 90°,
sinα.sinβ = (cos(α-β)
- cos(90°)) / 2 = (cos(α-β) - 0) / 2 = cos(α-β) / 2.
So, max(cos(α-β)) = 1,
if α = β = 45°. min(cos(α-β)) = 0, if α = 90°,
β = 0°, or β = 90°, α = 0°.