பின்வருவனவற்றை மதிப்பிடுக:

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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Detailed Solution

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கொடுக்கப்பட்டது:

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

பயன்படுத்தப்படும் சூத்திரம்:

cos (a - b) = cos a cos b + sin a sin b.

sin (90 - a) = cos a

கணக்கீடு:

⇒ 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)

⇒ cos (A - B) முற்றொருமையைப் பயன்படுத்துதல்,

⇒ cos(54 + A - 54 + A) = cos(2A)

எனவே, cos (36° - A) cos (36° + A) + cos (54° - A) cos (54° + A) இன் மதிப்பு cos(2A) ஆகும்.

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