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Question

Evaluate:
sec2(tan12)+cosec2(cot13)

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Solution

Now,

sec2(tan12)+cosec2(cot13)


=1+tan2(tan12)+1+cot2(cot13) [ Since sec2θ=1+tan2θ and cosec2θ=1+cot2θ]

=1+(tan(tan12))2+1+(cot(cot13))2

=1+22+1+32

=15.

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