1.

If sin θ + sin² θ = 1 , prove that cos² θ + cos⁴ θ = 1

Answer»

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



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