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    Which of the following options is NOT a correct trigonometric identity?
    Question

    Which of the following options is NOT a correct trigonometric identity?

    A.

    1 + cot² θ = cosec² θ

    B.

    1 + tan² θ = sec² θ

    C.

    1 - sin² θ = cos² θ

    D.

    cos² θ – sin² θ = 1

    Correct option is D

    Formula used: 
    sin2θ+cos2θ=1sec2θ=1+tan2θ1+cot2θ=cosec2θ\sin^2\theta + \cos^2 \theta =1 \\ \sec^2 \theta = 1 + \tan^2 \theta \\ 1+\cot^2 \theta = \cosec^2\theta​​
    Solution: 
    Checking from the options 
    option (a) is a  trigonometric identity.
    option (b) is a  trigonometric identity. 
    option (c) is a trigonometric identity.
    derive from sin2θ+cos2θ=1\sin^2\theta + \cos^2 \theta =1​​
    option (d) is not a a trigonometric identity 
    right identity is sin2θ+cos2θ=1\sin^2\theta + \cos^2 \theta =1 
    therefore, option(d) is correct.

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