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secA-cosecA)(1+tanA+cotA)=tanA secA-cotA cosecA

secA-cosecA)(1+tanA+cotA)=tanA secA-cotA cosecA

Grade:11

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Please find the answer to your question
(secA- cosecA)(1+ tanA+ cotA)
= (secA- cosecA+secAtanA- cosecAtanA+ secAcotA - cosecAcotA)
= (secAtanA- cosecAcotA) + secA- cosecA- cosecAtanA+ secAcotA
let us simplify
secA- cosecA- cosecAtanA+ secAcotA
= secA+ secAcotA - cosecA- cosecAtanA
= secA (1+cotA) - cosecA(1+tanA)
= (1/cosA)(1+(cosA/sinA)) - (1/sinA)(1+(sinA/cosA))
expanding and simplifying
= (1/cosA) +(1 /sinA)) - (1/sinA) -(1/cosA)
=0
so
(secAtanA- cosecAcotA) + secA- cosecA- cosecAtanA+ secAcotA
= (secAtanA- cosecAcotA) + 0
= (secAtanA- cosecAcotA)
= (tanA secA)- (cotA cosecA)

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