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In proving $\dfrac{\cot A-\cos A}{\cot A+\cos A}=\dfrac{\cosec A-1}{\cosec A+1}$, what is the first substitution made for $\cot A$?
A$\cot A=\dfrac{\sin A}{\cos A}$
B$\cot A=\dfrac{\cos A}{\sin A}$
C$\cot A=\dfrac{1}{\cos A}$
D$\cot A=\dfrac{1}{\sin A}$
Answer & Solution
Correct answer: B. $\cot A=\dfrac{\cos A}{\sin A}$
The proof starts by rewriting $\cot A$ in terms of sine and cosine: $\cot A=\frac{\cos A}{\sin A}$. This allows $\cos A$ to be factored from numerator and denominator, leading to expressions involving $\frac{1}{\sin A}=\cosec A$.
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