Question
Download Solution PDFIf sin (A + B) = cos (A + B), what is the value of tan A?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
sin (A + B) = cos (A + B)
Formula used:
sin (A + B) = sin A cos B + cos A sin B
cos (A + B) = cos A cos B - sin A sin B
Calculation:
sin (A + B) = cos (A + B)
sin A cos B + cos A sin B = cos A cos B - sin A sin B
sin A cos B + sin A sin B = cos A cos B - cos A sin B
sin A(cos B + sin B) = cos A (cos B - sin B)
sin A/cos A = (cos B - sin B)/(cos B + sin B)
sin A/cos A = (1 - sin B/cos B)/(1 + sin B/cos B)
tan A = (1 - tan B)/(1 + tan B)
∴ Option 1 is the correct answer.
Last updated on Jun 11, 2025
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