Question

if cosA +cos^2A=1 then sin^2+sin^4A=?
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Answer 1

Answer:

Sin²A + Sin⁴A = 1

Step-by-step explanation:

1.

I HOPE IT HELPS U

Answer 2

★ Answer:-

Sin²A+Sin⁴A=1

★ Concept:-

Here in this question, concept of trigonometry is used. We have given that Cos A+ Cos²A=1 and we have to find value of Sin²A+Sin⁴A. To solve the required problem we can use different trigonometric Identities and put value from 1st equation in the required equation.

So let's start!!

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★ Identity Used:-

• Sin²A+Cos²A=1

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★ Solution:-

We have identify:

⇒ Sin²A+Cos²A=1

By arranging it:

⇒Sin²A=1-Cos²A...(1)

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Now we have given equation:

⇒ Cos A+ Cos²A=1

⇒ Cos A=1-Cos²A...(2)

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Now:-

$\sf :\implies$ Sin²A+Sin⁴A

Taking Sin²A common

$\sf :\implies$ Sin²A+Sin⁴A=Sin²A (1+Sin²A)

By putting values from equation (1).

$\sf :\implies$ Sin²A+Sin⁴A=1-Cos²A(1+{1-Cos²A})

By putting values from equation (2).

$\sf :\implies$ Sin²A+Sin⁴A= Cos A(1+Cos A)

$\sf :\implies$ Sin²A+Sin⁴A= CosA+Cos²A

By putting values from given equation:

 $\sf :\implies$ Sin²A+Sin⁴A=1

∵  Sin²A+Sin⁴A=1.

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★ More Identities:-

• 1+Tan²A=Sec²A

• Sec²A-Tan²A=1

• 1+Cot²A=Cosec²A

• Cot²A=Cosec²A-1

• Sec²A=1-Cos²A

• Cos²A=1-Sec²A

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