Question
Download Solution PDFEvaluate the following:
cos(36° + A).cos(36° - A) + cos(54° + A).cos(54° - A)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
cos (36° - A) cos (36° + A) + cos (54° - A) cos (54° + A)
Formula used:
cos (a - b) = cos a cos b + sin a sin b.
sin (90 - a) = cos a
Calculation:
⇒ sin[90 – (36 – A)]sin[90 – (36 + A)] + cos (54° – A) cos (54° + A)
⇒ sin(54º + A)sin(54º – A) + cos (54° – A)cos (54° + A)
⇒ Using the identity cos(A – B),
⇒ cos(54 + A – 54 + A) = cos(2A)
Therefore, the value of cos (36° - A) cos (36° + A) + cos (54° - A) cos (54° + A) is cos(2A).
Last updated on Jun 9, 2025
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