If sinA + Sin2A = 1

Then prove that  Cos2A + Cos4A = 1

Now from the first equation , sinA + sin2A = 1

sinA = 1 - sin2

Using the identity( sin2A  = 1 - cos2A) we get ,

sinA = cos2A

Substitute this value in the first equation , u get

sinA + sin2A = 1

cos2A + (cos2A)2 = 1

cos2A + Cos4A = 1

Hence Proved.

(HAPPY TO HELP..........!!    :D)

  • 92

ssd

  • -7

 sinA = 1-sin^2(A) = cos^2(A)

Substitute in the proof eqn that is cos^2(A) + cos^4(A) to get sinA + sin^2(A) which is again 1.

QED

  • 0

Thanx for helping me

  • 13

We have,

sinA + sin2 A = 1 ...(1)

⇒ sinA = 1 sin2 A ...(2)

Now

cos2 A + cos4 A

= (1 sin2 A) + {(1 sin2 A)}2

= sinA + sin2 A [from (2)]

= 1 [from (1)]

  • 11

SIN A + SIN 2 A = 1 = > SIN 2 A = 1 - SINA =( COS2 A + SIN 2 A) - SINA

= > SIN 2 A = COS2 A + SIN 2 A - SINA

= > COS2 A -SINA = 0

= > COS2 A = SINA

NOW

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

cos2A + cos4A = COS2 A ( 1 + COS2 A)

=> cos2A + cos4A = SIN A ( 1 + SINA ) = SINA + SIN 2 A = 1 GIVEN

HENCE cos2A + cos4A = 1

  • 1
What are you looking for?