Question

What is the value of $(\text{cosec}A-\sin A)(\sec A-\cos A)(\tan A+\cot A)$?

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (B)

1

the value of $(\text{cosec}A-\sin A)(\sec A-\cos A)(\tan A+\cot A)$ is

$=(\frac{1}{\sin A}-\sin A)(\frac{1}{\cos A}-\cos A)(\frac{\sin A}{\cos A}+\frac{\cos A}{\sin A})$

$=\left(\frac{1-{\sin }^{2}A}{\sin A}\right)\left(\frac{1-{\cos }^{2}A}{\cos A}\right)\left(\frac{{\sin }^{2}A+{\cos }^{2}A}{\cos A\sin A}\right)$

$=\frac{{\cos }^{2}A\cdot {\sin }^{2}A\cdot 1}{\sin A\cdot \cos A\cos A\sin A}$