Question :- prove , tan¢ / (sec¢ - 1) + tan¢ /(sec¢ +1) = 2cosec¢
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Solution:- From LHS
⟹ tan¢ / (sec¢ - 1) + tan¢ /(sec¢ +1)
⟹ tan¢ ( sec¢ +1) + tan¢ ( sec¢ - 1) / (sec¢-1)(sec¢-1)
⟹ tan¢ * sec¢ + tan¢ + tan¢sec¢ - tab¢ /(sec²¢ -1)
⟹ 2tan¢ * sec¢ / (sec²¢ - 1)
∵ sec²¢ - tan²¢ = 1
⟹ ∴2tan¢ * sec¢ /tan²¢
⟹ 2sec¢ /tan¢
We know , sec¢ = 1/cos¢ and tan¢ = sin¢/cos¢
∴ 2/cos¢×cos¢/sin¢
⟹ 2/sin¢
∵ 1/sin¢= cosec¢
⟹ ∴ 2/sin¢ = 2cosec¢
So, proved , LHS =RHS
Step-by-step explanation:
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Question :- prove , tan¢ / (sec¢ - 1) + tan¢ /(sec¢ +1) = 2cosec¢
___________________________
Solution:- From LHS
⟹ tan¢ / (sec¢ - 1) + tan¢ /(sec¢ +1)
⟹ tan¢ ( sec¢ +1) + tan¢ ( sec¢ - 1) / (sec¢-1)(sec¢-1)
⟹ tan¢ * sec¢ + tan¢ + tan¢sec¢ - tab¢ /(sec²¢ -1)
⟹ 2tan¢ * sec¢ / (sec²¢ - 1)
∵ sec²¢ - tan²¢ = 1
⟹ ∴2tan¢ * sec¢ /tan²¢
⟹ 2sec¢ /tan¢
We know , sec¢ = 1/cos¢ and tan¢ = sin¢/cos¢
∴ 2/cos¢×cos¢/sin¢
⟹ 2/sin¢
∵ 1/sin¢= cosec¢
⟹ ∴ 2/sin¢ = 2cosec¢
So, proved , LHS =RHS
Step-by-step explanation:
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