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प्रश्न
Without using trigonometrical tables, evaluate:
`cosec^2 57^circ - tan^2 33^circ + cos 44^circ cosec 46^circ - sqrt(2) cos 45^circ - tan^2 60^circ`
उत्तर
`cosec^2 57^circ - tan^2 33^circ + cos 44^circ cosec 46^circ - sqrt(2) cos 45^circ - tan^2 60^circ`
= `cosec^2 (90^circ - 33^circ) - tan^2 33^circ + cos 44^circ cosec(90^circ - 44^circ) - sqrt(2) cos45^circ - tan^2 60^circ`
= `sec^2 33^circ - tan^2 33^circ + cos 44^circ sec 44^circ - sqrt(2) cos 45^circ - tan^2 60`
= `1 + 1 - sqrt(2) cos 45^circ - tan^2 60`
= `1 + 1 - sqrt(2)(1/(sqrt2)) - (sqrt3)^2`
= 2 – 1 – 3
= – 2
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