Question

If ΔABC, sinA + cosB = 0 then range of angle A is

(a) [0,(π/4)]

(b) [0, (π/6)] 

(c) [0, (π/3)] 

(d) [(π/6), (π/4)]

Answer 1

The correct option (a) [0, (π/4)]  

Explanation:

in ΔABC, sinA + cosB = 0

∴ sinA = – cos B ⇒ sin A = – sin[(π/2) – B] 

∴ A = B – (π/2) ⇒ B = (π/2) + A  

in ΔABC, A + B + C = π 

∴ C = π – [(π/2) + A + A]  

∴ C = (π/2) – 2A  

∴ A = (π/4) – (C/2)  

∴ range of A is [0, (π/4)].