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
Answers
Answered by
6
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.
Answered by
1
Answer:
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