Q238
What is the value of the expression cos2Acos2B + sin2(A - B) - sin2(A + B)?
A.
sin(2A - 2B)
B.
sin(2A + 2B)
C.
cos(2A + 2B)
AnswerD.
cos(2A - 2B)
Answer: Option C
Solution
Answer: Option C
Solution:
cos2Acos2B + sin2(A - B) - sin2(A + B)= cos2Acos2B + [{sin(A - B) + sin(A + B)}{sin(A - B) - sin(A + B)}]
= cos2Acos2B + [(sinAcosB - cosAsinB + sinAcosB + cosAsinB)(sinAcosB - cosAsinB - sinAcosB - cosAsinB)]
= cos2Acos2B + [(2sinAcosB) × (-2cosAsinB)]
= cos2Acos2B - (2sinAcosA) × (2sinBcosB)
= cos2Acos2B - sin2Asin2B
= cos(2A + 2B)
Alternate:
cos2Acos2B + sin2(A - B) - sin2(A + B)
= cos2Acos2B + sin2Asin2B
= cos(2A + 2B)