if acostheta – bsintheta =c prove that (asintheta + bcostheta)= +-✓a^2+b^2+c^2​

Question

if acostheta – bsintheta =c prove that (asintheta + bcostheta)= +-✓a^2+b^2+c^2​

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Hadley 2 months 2021-07-30T02:45:02+00:00 1 Answers 0 views 0

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    2021-07-30T02:46:46+00:00

    Answer:

    Instead of theta I had used ‘A’.

    Step-by-step explanation:

    acosA -bsinA= c

    squaring both sides

    a²cos²A +b²sin²A-2abcosAsinA=c ________(1)

    a²sin²A +b²cos²A+ 2absinAcosA = (asinA+bcosA)² _____(2)

    adding 1 and 2

    a²cos²A + b²sin²A-2abcosAsinA + a²sin²A +b²cos²A+ 2absinAcosA = c+ (asinA+bcosA)²

    (a²+b²)cos²A +(a²+b²)sin²A = c+ (asinA+bcosA)²

    (a²+b²)(cos²A+sin²A)-c = (asinA+bcosA)²

    We know that sin²A+cos²A=1

    a²+b²-c = (asinA+bcosA)²

    ±√(a²+b²-c) = asinA+bcosA

    asinA+bcosA = ±√(a²+b²-c)

    Hence proved.

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