Which of the following is a simplified form of the expression:

sinAcosA(tanA – cotA), where (0° ≤ A ≤ 90°)?

Correct option is B

Given:

Expression: $$\sin A \cos A (\tan A - \cot A),$$​where $$0^\circ \leq A \leq 90^\circ$$​​

Formula Used:

sin²A + cos²A =1

$$\cot A = \frac{\cos A}{\sin A}$$​​

$$\tan A = \frac{\sin A}{\cos A}$$​

Solution:

​$$\sin A \cos A (\tan A - \cot A)$$​​
$$=\sin A \cos A\left( \frac{\sin A}{\cos A} - \frac{\cos A}{\sin A}\right)$$​​
$$=\sin A \cos A \times\frac{\sin^2 A - \cos^2 A}{\sin A \cos A}$$​​

= $$\sin^2 A - \cos^2 A$$​

= $$\sin^2 A – 1 +\sin^2 A$$​​

​$$= 2\sin^2 A -1$$​​