Question

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Answer 1

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

Answer 2

Step-by-step explanation:

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