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Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(vii) (sin θ – 2sin3θ)/(2cos3θ-cos θ) = tan θ. Q.5(7)

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What is the best solution of the trigonometry question of class 10 ncert. Find the best way to solve this tricky question of exercise 8.4 please help me to solve this question in a easy way . Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(vii) (sin θ – 2sin3θ)/(2cos3θ-cos θ) = tan θ.

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  1. (sin θ – 2sin3θ)/(2cos3θ-cos θ) = tan θ

    L.H.S. = (sin θ – 2sin3θ)/(2cos3θ – cos θ)

    Take sin θ as in numerator and cos θ in denominator as outside, it becomes

    = [sin θ(1 – 2sin2θ)]/[cos θ(2cos2θ- 1)]

    We know that sin2θ = 1-cos2θ

    = sin θ[1 – 2(1-cos2θ)]/[cos θ(2cos2θ -1)]

    = [sin θ(2cos2θ -1)]/[cos θ(2cos2θ -1)]

    = tan θ = R.H.S.

    Hence proved

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