Question

if sin A +sin²A =1 then evaluate cos²A+ cos⁴ ​

Answer 1

Answer:

1

Step-by-step explanation:

$FORMULA\\\\sin^2x+cos^2x=1\\\\=>cos^2x=1-sin^2x\\\\=>Given\\\\sinA+sin^2A=1\\\\=>sinA=1-sin^2A\\\\=>sinA=cos^2A\\\\Now\\\\\\cos^2A+cos^4A\\\\=sinA+(sinA)^2\\\\=sinA+sin^2A\\\\=1$

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Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given a trigonometric expression
• sin A + sin² A = 1

To Find:

• We have to find the value of the given trigonometric expression
• cos² A + cos⁴ A

Solution:

We have been given that

$\large\boxed{\sf{\red{sin \: A + sin^2 \: A = 1 }}}$

$\implies \sf{sin \: A = 1 - sin^2 \: A}$

$\implies \sf{sin \: A = cos^2 \: A }$

$\implies \boxed{\sf{cos^2 \: A = sin \: A }}$ -------------------- ( 1 )

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$\large\underline{\sf{\orange{We \: have \: to \: find \: the \: value \: of}}}$

$\implies \sf{cos^2 \: A + cos^4 \: A }$

$\implies \sf{cos^2 \: A( 1 + cos^2 \: A ) }$

Substituting the value of cos² A

$\implies \sf{sin \: A( 1 + sin \: A ) }$

$\implies \sf{sin \: A + sin^2 \: A }$

$\implies \sf{1 }$

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{\purple{ cos^2 \: A + cos^4 \: A = 1}}}$

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$\boxed{</p><p></p><p>\begin{minipage}{6 cm}</p><p></p><p>Fundamental Trigonometric Identities \\ \\</p><p></p><p> \sin^2\theta + \cos^2\theta=1 \\ \\</p><p></p><p>1+\tan^2\theta = \sec^2\theta \\ \\</p><p></p><p>1+\cot^2\theta = \text{cosec}^2 \, \theta </p><p></p><p>\end{minipage}}$

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