12. Without using trigonometrical t...
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12. Without using trigonometrical tables, evaluate: cosec2 57° - tan2 330 + cos 440 cosec 46° - 72 cos 45º – tan2 60° [2016] S sa coba

11th - 12th Class
Maths
Solution
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( begin{aligned} operatorname{cosec}^{2} 57^{circ} &=operatorname{cosec}^{2}(90-57)=sec ^{2} 33 sec ^{2} 33-tan ^{2} 33+cos 44 operatorname{cosec} 46^{circ}-sqrt{2} cos 45-tan ^{2} 60 =& 1+cos 9982left(49-sqrt{2} times frac{1}{sqrt{2}}-(sqrt{3})^{2}right.=& 1+1-1-3 =& 2-4 -&-2 text { Ans. } end{aligned} )
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