Question

The value of the expression $[\text{cosec(}{75}^{\circ }+\theta )-\sec ({15}^{\circ }-\theta )-\tan ({55}^{\circ }+\theta )+\cot ({35}^{\circ }-\theta )]$ is

• A. $-1$
• B. $0$
• C. $1$
• D. $\frac{3}{2}$

Answer 1

Answer: (B)

$0$

$cosec({75}^0+\theta )-\sec ({15}^0-\theta )-\tan ({55}^0+\theta )+\cot ({35}^0-\theta )$
$=\sec ({90}^0-{75}^0-\theta )-\sec ({15}^0-\theta )-\cot ({90}^0-{55}^0-\theta )+\cot ({35}^0-\theta )$
$=\sec ({15}^0-\theta )-\sec ({15}^0-\theta )-\cot ({35}^0+\theta )+\cot ({35}^0+\theta )$
$=0$