Question

hey

if sin theta + sin2 theta = 1 then cos2 theta + cos4 theta = ?

Answer 1

Answer :-

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• Given :-

sinθ + sin²θ = 1

• To find :-

The value of : cos²θ + cos⁴θ

• Salutation :-

sinθ + sin²θ = 1

sinθ = 1 - sin²θ

sinθ = cos²θ ---------- ( i )

[ • As sin²θ + cos²θ = 1
So , sin²θ = 1 - cos²θ ]

★ Method - 1

sinθ = cos²θ

( sinθ )² = ( cos²θ )²

sin²θ = cos⁴θ

1 - cos²θ = cos⁴θ

cos⁴θ + cos²θ = 1 [ ★ Required answer ]

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★ Method - 2

cos²θ + cos⁴θ

= sinθ + ( sinθ )²

[ • Putting the value of cos²θ = sinθ ]

= sinθ + sin²θ

= 1 [ • Given , sinθ + sin²θ = 1 ]

• So finally ,

[ cos²θ + cos⁴θ = 1 ]

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★ Be Brainly ★

Answer 2

Heya..

Here is your answer...

Given,

sinθ + sin^2 θ = 1

or, sinθ + sin^2 θ = sin^2 θ + cos^2 θ

or, cos^2 θ= sin θ, ….(1) , squaring both side

or, cos^4 θ = sin^2 θ ….(2) , adding equation (1) & (2),

cos^2 θ+cos^4 θ = sin θ + sin^2 θ = 1 ( given)

Therefore cos^2 θ + cos^4 θ= 1

Itmay help you...☺☺