Answer :

Given: cos A + cos2 A = 1


Therefore cos A = 1 – cos2 A = sin2 A ……(1)


Now, consider sin2A + sin4A = sin2 A(1 + sin2A)


Put the value of sin2A in the above equation:


Therefore, sin2A + sin4A = sin2 A(1 + sin2A)


= (1 – cos2 A)(1+1 – cos2 A)


Again, from equation (1), we have 1 – cos2 A = cos A. So put the value of cos A in the above equation:


Therefore, sin2A + sin4A = (cosA)(1+ cosA)


= cos A + cos2 A


= 1 (given)


Therefore, sin2A + sin4A = 1

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