Question

If cos(A + B)= 1/2 and sin(A - B)= 1/2 and 0°<
A +Bs 90°, A>B, then the value of B is
A. 15
B. 45
C. 60
D. 30​

Answer 1

Answer:

B. 45

Step-by-step explanation:

cos(A+B) = 1/2

⇒cos (A+B) = cos(60)  (as 0<A+B<90)

⇒A+B = 60

sin(A-B) = 1/2

⇒sin(A-B) = sin(30) or sin (150)

⇒A-B = 30 or 150

Case:1

A - B = 30

A + B = 60

Solving we get, A = 45 and B = 15

A>B is satisfied.

Case:2

A - B = 150

A + B = 60

Solving, we get A = 105, B = -45

A>B is satisfied.

So the value of A can be 45 or 105.

Answer 2

Answer:

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