Question

(sec 14 -cot 76)(sec 14 +cot 76)

Answer 1

We have,

( sec14° - cot76° ) ( sec14° + cot76° )

since,

cot ( 90 - A) = tan A

therefore,

( sec 14° - tan 14° ) ( sec14° + tan 14° )

using identity

( a - b) (a+ b) = a^2 - b^2

we will get

sec^(2) 14° - tan^(2) 14°

using identity

sec^(2) A - tan^(2) A = 1

we will get

= 1 . ( Ans.)