If sinA + sin2A = 1 then what is the value of cos2A + cos4A?

If sinA + sin2A = 1 then what is the value of cos2A + cos4A? Correct Answer 1

Given:

sinA + sin2A = 1

Formula used:

cos2A = 1 – sin2A

Calculation:

sinA + sin2A = 1      ----(i)

⇒ sinA = 1 – sin2A

⇒ sinA = cos2A      ----(ii)

⇒ sin2A = cos4A      ----(iii)

Now, we have to find cos2A + cos4A

From equation (ii) and (iii), we get

⇒ cos2A + cos4A = sinA + sin2A

⇒ cos2A + cos4A = 1   

∴ cos2A + cos4A is 1.