Question

prove that sin8A/sinA= 8cosAcos2Acos4A

Answer 1

$\Large\bold{\boxed{\boxed{Your\:Question}}}$ :--

prove that :---- (sin8A/sinA) = 8cosAcos2Acos4A

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We know that :--

sin2A = 2sinA*CosA

using this formula ,

Sin8A/sinA

=> sin(2*4A)/sinA

=> (2sin4A*cos4A)/sinA

=> 2sin(2*2A)*cos4A/sinA

=> 2(2sin2A*cos2A)*cos4A/sinA

=> 4sin2A*cos2A*cos4A/sinA

=> 4(2sinA*cosA)cos2A*cos4A/sinA

=> 8sinA*cosA*cos2A*cos4A/sinA

=> 8cosA*cos2A*cos4A $\huge\blue{</strong><strong>PROVED</strong><strong>}$

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$\Large\bold{\boxed{\boxed{ADDITIONAL\:BRAINLY\:INFORMATION\:-:}}}$ :------

Cos2A = 2cos²A-1 = 1-2Sin²A

Tan2A = 2TanA/(1-tan²A)