If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ

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Q) If θ is an acute angle and sin θ = cos θ, find the value of tan² θ + cot² θ – 2.

Ans:

tan² θ + cot² θ – 2.

= $\frac{\sin^2\theta}{\cos^2\theta}$ + $\frac{\cos^2\theta}{\sin^2\theta}$ – 2

By sin θ = cos θ (given),

= $\frac{\sin^2\theta}{\sin^2\theta}$ + $\frac{\sin^2\theta}{\sin^2\theta}$ – 2

= 1 + 1 – 2

= 0

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