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Simplify cos(36 - A)cos(36 + A) + cos(54 - A)cos(54 +...

This question belongs to Arithmetic Ability Trigonometry
Trigonometry
?

Simplify: cos(36° - A)cos(36° + A) + cos(54° - A)cos(54° + A)

Answer & Solution
Correct Answer: Option C
cos(36° - A)cos(36° + A) + cos(54° - A)cos(54° + A)
= cos(36° - A)cos(36° + A) + sin(36° + A)sin(36° - A)
∵ cos(A - B) = cosA.cosB + sinA.sinB
= cos[36° - A - 36° - A]
= cos(-2A)
= cos2A
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