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2 solutions
Moderator note:
Can you solve this problem without knowing neither values of tan ( 7 5 ∘ ) , cot ( 7 5 ∘ ) ?
In response to the Challenge Master: Generalising,
tan θ + cot θ = cos θ sin θ + sin θ cos θ = sin θ cos θ sin 2 θ + cos 2 θ = 2 csc 2 θ
Use tan(A+B) formula
It's a simple process of elimination. If θ ∈ ( 0 , 2 π ) then tan θ > 0 , therefore cot θ > 0 . And it can't be 1, because then it would have to be 0 + 1 or the sum of two numbers in ( 0 , 1 ) , either of which is impossible if one is the reciprocal of the other.
They are not always greater than 0 between 0 n 90
Would you care to give a counterexample Ahmed?
=2+√3+2-√3=4