Consider the identity: $\frac{\cos \theta}{\sin \theta}-\frac{\cos 2 \theta}{\sin \theta \cdot \cos \theta}=\tan \theta$
3.1 Prove the identity.

Starting from the left side of the equation, apply the double-angle identity for cosine and simplify the fractions.
sin θ cos θ ​ − sin θ cos θ cos ( 2 θ ) ​ = tan θ . ;

Answered by jacob193 | 2025-07-10

To prove the identity, we start with s i n θ c o s θ ​ − s i n θ ⋅ c o s θ c o s 2 θ ​ and use the double-angle identity for cosine. Simplifying this expression step-by-step leads to the conclusion that it equals tan θ . Therefore, the identity holds true.
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Answered by jacob193 | 2025-07-17