📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!

    Question

    If 5 sinθ + 3 cosθ = 4 then value of 5 cosθ - 3 sinθ

    = ?
    A 2√3 Correct Answer Incorrect Answer
    B 3√2 Correct Answer Incorrect Answer
    C 4√3 Correct Answer Incorrect Answer
    D 2√2 Correct Answer Incorrect Answer

    Solution

    If 5 sinθ + 3 cosθ = 4 Let 5 cosθ - 3 sinθ = K Then squaring both equation and adding (5sinθ+3cosθ)^2 = (4)^2 (5cosθ-3sinθ)^2 = (K)^2 25 sin²θ + 9 cos²θ+ 30 sinθ cosθ = 16 ---------------------------------------------- 9 sin²θ + 25 cos²θ- 30 sinθ cosθ = K² 34 sin²θ + 34 cos²θ = 16 + K² 34 (sin²θ + 34 cos²θ) = 16 + K²    { sin²θ + cos²θ = 1} 34 = 16 + K² K² = 34 - 16 = 18 K = √18 = ± 3√2

    Practice Next
    More Trigonometry Questions

    Relevant for Exams:

    ask-question