Question

The value of $\csc ({65}^0+\theta )-\sec ({25}^0-\theta )-\tan ({55}^0-\theta )+\cot ({35}^0+\theta )$ is

• A. $0$
• B. $-1$
• C. $\theta +90$
• D. None of these

Answer 1

Answer: (A)

$0$

Given, $\csc ({65}^{\circ }+\theta )-\sec (25-\theta )-\tan (55-\theta )+\cot (35+\theta )$
$=\csc ({90}^{\circ }-{25}^{\circ }+\theta )-\sec ({25}^{\circ }-\theta )-\tan ({55}^{\circ }-\theta )+\cot ({90}^{\circ }-{55}^{\circ }+\theta )$
$=\csc ({90}^{\circ }-({25}^{\circ }-\theta \left)\right)-\sec ({25}^{\circ }-\theta )-\tan ({55}^{\circ }-\theta )+\cot ({90}^{\circ }-({55}^{\circ }-\theta \left)\right)$
$=\sec ({25}^{\circ }-\theta )-\sec ({25}^{\circ }-\theta )-\tan ({55}^{\circ }-\theta )+\tan ({55}^{\circ }-\theta )$
$=0$