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Question

If sin A + sin2 A + sin3 A = 1; then find cos6 A – 4 cos4 A + 8 cos2 A -


  1. 3

  2. 2

  3. 1

  4. - 1

  5. 4


Solution

The correct option is E

4


 sinA+sin2A+sin3A=1sinA+sin2A+sin3A=cos2A+sin2A.........(1=cos2A+sin2A)sinA+sin3A=cos2AsinA(1+sin2A)=cos2AsinA(1+1cos2A)=cos2ASquaring both sides sin2A(2cos2A)2=cos4A(1cos2A)(4+cos4A4cos2A)=cos4A4+cos4A4cos2A4cos2Acos6A+4cos4A=cos4A4=cos6A4cos4Acos4A+cos4A+4cos2A+4cos2Acos6A4cos4A+8cos2A=4

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