Question
Download Solution PDFFind the value of cos 2A cos 2B + sin2(A - B) - sin2(A + B)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
cos 2A cos 2B + sin2(A - B) - sin2(A + B)
Concept used:
cos (a + b) = cos a cos b - sin a sin b
sin2a - sin2b = sin(a + b) sin(a - b)
Calculation:
cos 2A cos 2B + sin2(A - B) - sin2(A + B)
⇒ cos 2A cos 2B - [sin2(A + B) - sin2(A - B)]
{sin2a - sin2b = sin(a + b) sin(a - b)}
⇒ cos 2A cos 2B - [sin(A + B + A - B) sin(A + B - A + B)]
⇒ cos 2A cos 2B - [sin(A + A) sin(B + B)]
⇒ cos 2A cos 2B - sin 2A sin 2B
⇒ cos (2A + 2B)
∴ The required answer is cos (2A + 2B).
Last updated on Jul 14, 2025
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