Question

Express $(sin{75}^{\circ }+cosec{75}^{\circ })$ in terms of trigonometric ratios of angles between $0^{\circ }$ and ${15}^{\circ }.$

• A. $(sec{15}^{\circ }+sin{15}^{\circ })$
• B. $(cos{45}^{\circ }+sec{45}^{\circ })$
• C. $(cos{15}^{\circ }+sec{15}^{\circ })$
• D. $(cos{25}^{\circ }+sec{25}^{\circ })$

Answer 1

The correct option is C $(cos{15}^{\circ }+sec{15}^{\circ })$

$\Rightarrow sin{75}^{\circ }+cosec{75}^{\circ }$

$=sin({90}^{\circ }-{15}^{\circ })+cosec({90}^{\circ }-{15}^{\circ })$

$=(cos{15}^{\circ }+sec{15}^{\circ })$