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

Question

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

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Melody 3 weeks 2021-09-04T19:12:51+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-04T19:14:02+00:00

    \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 )

    _________________________________

    \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 }

    __________________________________

    \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}}}

    ___________________________________

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

    ____________________________________

    0
    2021-09-04T19:14:31+00:00

    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\\\\

    HOPE IT HELPS

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