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

By Hadley

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

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Hadley

4. Prove:
+
(i) (x – y – 2)2 – (x2 + y2 + z2) = 2(yz – zx – xy)
(ii) (3p – 5q)2 – (3p + 5)2 + 60pq = 0
(iii) (

a sum of money amounts to rs
9360 in 7 years at 8% simple
interest. will it double itself at the
same rate.​

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

  1. 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.

    Reply

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