Evaluate (5/cot2 30) + (1/ sin2 60) - cot2 45 + 2 sin2 90

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Q) Evaluate (5/cot² 30^°) + (1/ sin² 60^°) – cot² 45^° + 2 sin² 90^°

Ans:

Givent that, $\frac{5}{\cot^2 30} + \frac{1}{\sin^2 60}$ – cot² 45 + 2 sin² 90

= $\frac{5}{(\sqrt3)^2}$ + $\frac{1}{(\frac{\sqrt3}{2})^2}$ – (1)²+ 2 (1)²

= $\frac{5}{3}$ + $\frac{4}{3}$ – 1+ 2

= 3 – 1+ 2

= 4

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