Question

 If sin θ + sin² θ = 1, then cos² θ + cos⁴ θ =

– 1

1

0

None of These

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Answer 1

Answer:

sin (theta) +sin ^2 (theta) =1

sin (theta) +1-cos ^2 (theta) =1

sin (theta) -cos ^2 (theta) =0

sin (theta) =cos ^2 (theta)

square both sides

sin^2 (theta) =cos ^4 (theta)

1-cos ^2 (theta)= cos ^4 (theta)

cos ^4 (theta)+cos ^2 (theta)=1

ANS:1

Answer 2

$\huge\underline\mathbb{\red S\pink{O}\purple{L} \blue{UT} \orange{I}\green{ON :}}$

★ Given that,

• sin θ + sin² θ = 1

★ To find,

• cos² θ + cos⁴ θ = ?

★ Let,

➡ sin θ + sin² θ = 1 ..... (1)

➡ sin θ = 1 - sin² θ

• 1 - sin² θ = cos² θ

➡ sin θ = cos² θ ..... (2)

★ Now,

➡ cos² θ + cos⁴ θ

➡ cos² θ + (cos² θ)²

• Substitute the value of (2) cos² θ = sin θ

➡ sin θ + (sin θ)²

➡ sin θ + sin² θ = 1

$\underline{\boxed{\bf{\purple{∴ Hence, \:the\:value\:of\:cos²\:θ\:+\:cos⁴\:θ\:=\:1}}}}$

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