Question

Sin(a-b)=1/2 and cos(a+b)=1/2, where a and b are positive acute angles, then

Answer 1

Answer:

a=45 , b=15

Step-by-step explanation:

we know that sin30°=1/2

so a-b=30... .. .. .. . (1)

cos 60°=1/2

so a+b=60 ...........(2)

add (1) and (2) we get

a-b+a+b=30+60

2a=90

a=45

and b=15

Answer 2

Answer:

a = 45° , b = 15°

Step-by-step explanation:

Also sin 30° = 1

2

cos60° = 1

2

Therefore,

a - b = 30° ————> 1

a + b = 60° ————>2

Adding 1 and 2

a - b + a + b = 30 + 60

2a = 90

a = 90

2

a = 45°

Substitute a = 45° in Equation 2

a + b = 60

45 + b = 60

b = 60 - 45

b = 15°

Therefore, a = 45°, b = 15°

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