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Question

Prove that sec2(tan12)+cosec2(cot13)=15.

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Solution

We know, tan1x=sec1(x2+1) and cot1x=cosec1(x2+1)
So, sec2(tan12)+cosec2(cot13)
=sec2(sec15)+cosec2(cosec110)
=(sec(sec15))2+(cosec(cosec110))2
=5+10 (since both 5 and 10 are greater than 1)
=15

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