Evaluate each of the following

$(c o s e c^{2} 45^{o} s e c^{2} 30^{o}) (s i n^{2} 30^{o} + 4 c o t^{2} 45^{o} - s e c^{2} 60^{o})$

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Solution

(cosec2 45o sec2 30o)(sin2 30o+4 cot2 45o−sec2 60o)
=(2½²2/3½²)(1/2²+41-2)
=6

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Similar questions

$(s i n^{2} 30^{\circ} + 4 c o t^{2} 45^{\circ} - s e c^{2} 60^{\circ}) (c o s e c^{2} 45^{\circ} s e c^{2} 30^{\circ})$

(c o s e c^{2} 45^{\circ} s e c^{2} 30^{\circ}) (s i n^{2} 30^{\circ} + 4 c o t^{2} 45^{\circ} - s e c^{2} 60^{\circ})

\frac{1}{4}

{cos}^{2} 60^{\circ} {sin}^{2} 30^{\circ} + {tan}^{2} 30^{\circ} {cot}^{2} 60^{\circ}

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