Evaluate the following:

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

This question was previously asked in
SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 2)
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  1. sin 2A
  2. cos A
  3. sin A
  4. cos 2A

Answer (Detailed Solution Below)

Option 4 : cos 2A
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PYST 1:SSC CGL 2023 - Quantitative Aptitude(Held On:14 Jul 2023 Shift 1)
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Detailed Solution

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Given:

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).

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