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We know tan²x + 1 = sec²x…(1)

Let tan x be a and sec x be b

According to question

a + b =k

Manipulating and Substituting in 1 we get

⇒ a² – b² = -1

⇒ (a-b)( a + b) = -1

⇒ (a-b).k =-1

⇒ a-b = -k^-1

a + b =k

a-b = -k-¹

subtracting above equations we get

2b =k +k^-1