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    Question

    If θ is an acute angle and sin θ + cosec θ = 2, then

    the value of sin⁵ θ + cosec⁵ θ is:
    A 10 Correct Answer Incorrect Answer
    B 2 Correct Answer Incorrect Answer
    C 4 Correct Answer Incorrect Answer
    D 5 Correct Answer Incorrect Answer

    Solution

    Given – sin + cseccθ = 2, let x = sin θ, then cosec θ =1/x ATQ- x+1/x =2     x²+1 = 2x x²-2x+1 0 (x-1)2 = 0 x-1 =0 x =1. Thus, sin θ = 1, which means θ = 90°. Now, Sin 5 θ = 15=1 Similarly, Cosec5 θ = 1 Therefore, Sin 5 θ + Cosec5 θ =1+1=2 So, the value is 2.

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