Simplification of Given Equation :

On simplifying
math 35

we get

  1. sin3A
  2. cos 3A
  3. sin A + cos A
  4. 3
Anurag Mishra Professor Asked on 1st October 2015 in Maths.
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  • 1 Answer(s)

    Answer: (4) 3

    Explanation:-
    (Sin3A + Sin 3A)/Sin A + (Cos3A – Cos 3 A)/Cos A
    Formula –
    Sin 3A = 3 Sin A – 4 Sin3 A & Cos 3A = 4 Cos3A – 3 Cos A

    Then, put the value of Sin 3A & Cos 3A in given equation,
    Therefore, (Sin3 A + 3 Sin A – 4 Sin3 A)/Sin A + (Cos3 A – 4 Cos3 A + 3 Cos A)/Cos A
    = (3Sin A – 3 Sin3 A) / Sin A + (3 Cos A – 3 Cos3A)/ Cos A
    = 3 Sin A (1 – Sin2 A)/Sin A + 3 Cos A (1 – Cos2 A)/Cos A
    = 3 (1 – Sin2 A) + 3 ( 1 – Cos2A)
    = 3 Cos2 A + 3 (1 – cos2 A)
    = 3 (Cos2 A + 1 – Cos2A)
    = 3 x 1
    = 3
    Then, the value of given equation is 3.

    Hence, the answer is (4) 3.

    Anurag Mishra Professor Answered on 3rd October 2015.
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