Question

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

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

Answer 1

The correct option is B

0

$cosec({90}^{\circ }-x)=secx$

$tan({90}^{\circ }-x)=cotx$

$\left[cosec\right({75}^{\circ }+q)-sec({15}^{\circ }-q)-tan({55}^{\circ }+q)+cot({35}^{\circ }-q\left)\right]$

$=\left[cosec\right({75}^{\circ }+q)-cosec({75}^{\circ }+q)-tan({55}^{\circ }+q)+tan({55}^{\circ }+q\left)\right]$

$=0$