Question

(1+cotθ-cosecθ) (1+tanθ+secθ) = 2

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Answer 1

Answer:

L.H.S = ( 1+ cotA - cosec A ) ( 1+ tanA - secA)

Step-by-step explanation:

= ( 1+ cosA / sinA - 1/ sinA ) ( 1+ sinA /cosA - 1/cosA )

= ( sinA + cosA -1/sinA ) ( cosA + sinA - 1/cosA )

= ((sinA + cosA ) - ( 1 ) /sinA ) ((cosA + sinA ) - ( 1 ) /cosA )

= ((sinA + cosA )raise to power2 - (1)raise to power 2)/sinAcosA

= sin2A +cos2A +2sinAcosA - 1 /sinAcosA

= 1+2sinAcosA - 1/sinAcosA   (because sin2A + cos2A = 1)

= 2sinAcosA / sinAcosA

=2

Therefore, LHS = RHS

Hence Proved

Answer 2

Answer:

formula L.H.S=(1+cota-coseca) (1+tana-seca)

Step-by-step explanation:

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