Question
Download Solution PDFIf sin (a + b) = 1 and cos (a - b) = \(\frac{1}{2} \), then find a.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
sin(A + B) = 1 and cos(A - B) = 1/2
Formula used:
sin90° = 1
cos60° = 1/2
Calculation:
sin(A + B) = 1
⇒ sin(A + B) = sin90°
⇒ A + B = 90° ....(1)
Again,
cos(A – B) = 1/2
⇒ cos(A – B) = cos60°
⇒ A – B = 60° .....(2)
Adding equation (1) and (2), we get
⇒ A + B + A – B = (90° + 60°)
⇒ 2A = 150°
⇒ A = (150/2)
⇒ A = 75°
The value of a is 75°.
Last updated on Jul 21, 2025
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