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Rajan@2021
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If sin (A + B) = 1 and cos (A − B) = 1, 0° ≤ (A + B) ≤ 90° and A > B, then find A and B.

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This is the basic and conceptual question from trigonometric ratios in which we have been asked to calculate the value of angle A and B, if sin (A + B) = 1 and cos (A − B) = 1, 0° ≤ (A + B) ≤ 90° and A > B.

RS Aggarwal, Class 10, chapter 11, question no 23

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1 Answer

  1. Given, sin(A+B)=1

    cos(AB)=1
    0<A+B90 and AB,

    We know that, sin90=1 and cos0=1

    Consider,
    sin(A+B)=1 and sin90=1

    (A+B)=90   —————(i)

    Consider,
    cos(AB)=1 and cos0=1

    (AB)=0
    A=B   —————(ii)

    sub (ii) in (i)

    A+A=90
    2A=90
    A=45

    A=B=45

    A=B=45

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