Question
Question: Prove the following: \[\left[ 1+\cot \theta -\sec \left( \dfrac{\pi }{2}+\theta \right) \right]\cd...
Prove the following:
[1+cotθ−sec(2π+θ)]⋅[1+cotθ+sec(2π+θ)]=2cotθ
Explanation
Solution
We will simplify the left hand side of the given equation. We expect the simplified form of the LHS to be equal to the RHS in the given equation. We will use some trigonometric relations and identities to carry out the simplification. We will also use some algebraic identities to obtain the desired answer.
Complete step by step answer:
We will start with the left hand side that is L.H.S. We know that secant is the reciprocal of cosine. Substituting secant function with the cosine function, we get the following