Question

Express
$(cos{83}^{\circ }-sec{76}^{\circ })$
in terms of trigonometric ratios of angles between $0^{\circ }$ and ${45}^{\circ }.$

• A. $(sin{7}^{\circ }-cosec{14}^{\circ })$
• B. $(sin{17}^{\circ }-cosec{24}^{\circ })$
• C. $(cos{7}^{\circ }-cosec{14}^{\circ })$
• D. $(sin{17}^{\circ }-sec{14}^{\circ })$

Answer 1

The correct option is A $(sin{7}^{\circ }-cosec{14}^{\circ })$

$\Rightarrow cos{83}^{\circ }-sec{76}^{\circ }$

$=cos({90}^{\circ }-7^{\circ })-sec({90}^{\circ }-{14}^{\circ })$

$\because sinA=cos({90}^{\circ }-A)$;
$\because cosecA=sec({90}^{\circ }-A)$

$=(sin{7}^{\circ }-cosec{14}^{\circ })$