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Question
If tan θ – sin2θ = cos2θ, then show that `sin^2θ = 1/2`.
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Solution
tan θ – sin2θ = cos2θ ...[Given]
∴ tan θ = sin2θ + cos2θ
∴ tan θ = 1 ...[∵ sin2θ + cos2θ = 1]
But, tan 45° = 1
∴ tan θ = tan 45°
∴ θ = 45°
sin2θ = sin245°
= `(1/sqrt(2))^2`
= `1/2`
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