evaluate: tan^2( sec^-1 2)+ cot^2(cosec^-1 3)
Asked by meghna | 24th Jan, 2014, 10:13: PM
Expert Answer:
tan2(sec-12) = sec2(sec-12) - 1
cot2(cosec-13) = cosec2(cosec-13) - 1
Therefore,
tan2(sec-12) + cot2(cosec-13)
= sec2(sec-12) - 1 + cosec2(cosec-13) - 1
= [sec(sec-12)]2 + [cosec(cosec-13)]2 - 2
= (2)2 + (3)2 - 2
= 4 + 9 - 2
= 11
cot2(cosec-13) = cosec2(cosec-13) - 1
Therefore,
tan2(sec-12) + cot2(cosec-13)
= sec2(sec-12) - 1 + cosec2(cosec-13) - 1
= [sec(sec-12)]2 + [cosec(cosec-13)]2 - 2
= (2)2 + (3)2 - 2
= 4 + 9 - 2
= 11
Answered by | 26th Jan, 2014, 06:26: PM
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