If sin(a-b)=1/2 cos(a+b)=1/2 0 a+b 90 a b find a and b
Answers
Answer:
45° and 15°
Step-by-step explanation:
Given, Sin(a-b) =1/2, Cos (a+b) = 1/2, 0≤a+b≤90,a>b
Sin(a-b) = 1/2 | Cos(a+b) = 1/2
But we know that Sin30 = 1/2 | But we know that Cos60 = 1/2
Sin(a-b) = Sin 30 | Cos(a+b) = Cos60
a - b = 30 ------------[1] | a + b = 60 -------------- [2]
Solve [1] and [2] by addition
a - b = 30
a + b = 60
-----------------
2a = 90
=> a = 45°.
Substitute value of a in [1]
a - b = 30
45 - b = 30
=> b = 15°
Answer:
A = 45 and B = 15
Step-by-step explanation:
Since, sin (A-B) = 1/2 = sin = 30
=> A-B = 30 ----------------(1)
and cos (A+B) = 1/2 = cos 60
=> A+B = 60 -----------------(2)
solving (1) and (2)
=> A - B = 30 ------(1)
=> A + B = 60 -----(2)
From eq. (1)
=> A - B = 30
=> A = 30 - B ---------(3)
Substitute the value of A in eq. (2)
=> A + B = 60
=> (30+B) + B = 60
=> 30 + 2B = 60
=> 2B = 60 - 30
=> 2B = 30
=> B = 30/2
=> B = 15
putting the value of B in eq. (3)
=> A = 30 + B
=> A = 30 + 15
=> A = 45
Hence, A = 45 and B = 15