If tan θ – sin2θ = cos2θ, then show that sin2 θ = 12 - Geometry Mathematics 2

Question

If tan θ – sin²θ = cos²θ, then show that sin²θ = $\frac{1}{2}$ .

Sum

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°

= ${(\frac{1}{\sqrt{2}})}^{2}$

= $\frac{1}{2}$

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If tan θ – sin2θ = cos2θ, then show that sin2 θ = 12 - Geometry Mathematics 2

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