If cos A + cos2 A = 1 then (sin2A + sin4A) = ?
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