Question

If tan theta = 1/root5 , Evaluate: cosec2theta - cot2theta / cosec2theta + cot2 theta

Answer 1

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tanθ=31⇒tanθ=tan30∘⇒θ=30∘

cosec2θ+sec2θcosec2θ−sec2θ=cosec230∘+sec230∘cosec230∘−sec230∘

=22+(2/3)222−(2/3)2

=4+4/34−4/3=12+412−4=168=21