Question

sin(α-β)=1/2 and cos(α+β)= 1/2 where α,β is a acute triangle. to (a) α=45°,β=15° (b) α=15°, β=45° (c) α= 60° , β=15° (d) None of these

Answer 1

Answer:

(a) α=45°,β=15°

Step-by-step explanation:

sin(α-β)=1/2

sin(α-β)=sin 30

α-β=30---------------(i)

cos(α+β)=1/2

cos(α+β)=cos 60

α+β=60--------------(ii)

From (i) and (ii)

α-β=30

α+β=60

____________

2α=90

α=45

Sub in (i)

45-β=30

-β=-15

β=15