Question

Hey!!

If , sinθ + sin²θ=1 then cos²θ + cos⁴θ = ?

Answer 1

Here is your solution

If , sinθ + sin²θ=1---------------(1)
then cos²θ + cos⁴θ = ?

From equation (1)

sinθ + sin²θ=1

sin²θ=1-sinθ
(we know that sin²θ=1-cos²θ)

1-cos²θ=1-sinθ
cos²θ=sinθ
cos⁴θ =sin²θ
Now

cos⁴θ =sin²θ
cos⁴θ=1-cos²θ
cos²θ+cos⁴θ=1✔

hopeit helps you

Answer 2

Answer :-

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Given ,

sinθ + sin²θ = 1

To find ,

The value of : cos²θ + cos⁴θ

Now ,

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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