show that tan^2Q+cot^2Q = cosec^2 sec^2Q-2
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Step-by-step explanation:
tan²Q+cot²Q = cosec²Qsec²Q -2
tan²Q+cot²Q + 2 = cosec²Qsec²Q
tan²Q+cot²Q + 2tanQcotQ = cosec²Qsec²Q (tanQcotQ = 1)
(tanQ+cotQ)² = cosec²Qsec²Q
(sinQ/cosQ + cosQ/sinQ)² = cosec²Qsec²Q
((sin²Q + cos²Q) / cosQ sinQ)² = cosec²Qsec²Q
(1/cosQsinQ)² = cosec²Qsec²Q
(cosecQsecQ)² = cosec²Qsec²Q
cosec²Qsec²Q = cosec²Qsec²Q
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