Evaluate 2sec2 θ + 3 cosec2 θ - 2 sin θ cos θ if θ = 45.

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Q) Evaluate 2sec² θ + 3 cosec² θ – 2 sin θ cos θ if θ = 45⁰.

Ans: Since θ = 45⁰, sec 45⁰ = √2, cosec 45⁰ = √2, sin 45⁰ = $\frac{1}{\sqrt2}$ ; cos 45⁰ = $\frac{1}{\sqrt2}$

2sec² θ + 3 cosec² θ – 2 sin θ cos θ

= 2 (√2)² + 3 (√2)² – 2 $(\frac{1}{\sqrt2}) (\frac{1}{\sqrt2})$

= 4 + 6 – 1 = 9

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