Question

If sinA + sin²A = 1, prove that cos²A + sin⁴A = 1.​

Answer 1

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Now from the first equation , sinA + sin^2A = 1

sinA = 1 - sin^2A

Using the identity( sin^2A = 1 - cos^2A) we get ,

sinA = cos^2A

Substitute this value in the first equation , u get

sinA + sin^2A = 1

cos^2A + (cos2A)^2 = 1

cos^2A + Cos^4A = 1

Answer 2

Answer:

Now from the first equation ,

sinA + sin^2A = 1sinA = 1 - sin^2A

Using the identity( sin^2A = 1 - cos^2A) we get ,

sinA = cos^2A

Substitute this value in the first equation , u get

sinA + sin^2A = 1cos^2A + (cos2A)^2

= 1cos^2A + Cos^4A = 1

Hope it helps...

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