Question

establish the identity. tan u cot u - sin²u = cos²u. rewrite the factor cot u in the first term, tan u cot u, in terms of tan u. tan u·□ - sin²u

Explanation:

Step1: Recall the reciprocal relationship

We know that $\cot u=\frac{1}{\tan u}$. So we rewrite $\tan u\cot u$ as $\tan u\times\frac{1}{\tan u}$.
$\tan u\times\frac{1}{\tan u}-\sin^{2}u$

Step2: Simplify the first - term

Since $\tan u\times\frac{1}{\tan u}=1$, the left - hand side of the identity becomes $1 - \sin^{2}u$.
$1-\sin^{2}u$

Step3: Use the Pythagorean identity

By the Pythagorean identity $\sin^{2}u+\cos^{2}u = 1$, we can rewrite $1-\sin^{2}u$ as $\cos^{2}u$.
$\cos^{2}u$

Answer:

$\cos^{2}u$