Question

Evaluate :
sin^2 63°+ sin^2 27°/COS^2 17° + cos- 73°​

Answer 1

Correct Question :-

Evaluate -:

$\sf{\dfrac{{sin}^{2}{63}^{\circ} + {sin}^{2}{27}^{\circ}}{{cos}^{2}{17}^{\circ} + {cos}^{2}{73}^{\circ}}}$

Answer :-

$\sf{ \longrightarrow \: \: \dfrac{{sin}^{2}{63}^{\circ} + {sin}^{2}{27}^{\circ}}{{cos}^{2}{17}^{\circ} + {cos}^{2}{73}^{\circ}}}$

By putting the trigonometric ratio of complementary angle: [sin(90 - A) = cosA],

∴ sin63° = sin(90° - 27°) = cos27°

$\sf{ \longrightarrow \: \: \dfrac{{cos}^{2}{27}^{\circ} + {sin}^{2}{27}^{\circ}}{{cos}^{2}{17}^{\circ} + {cos}^{2}{73}^{\circ}}}$

By putting the trigonometric ratio of complementary angle: [cos(90 - A) = sin A],

∴ cos73° = cos(90° - 17°) = sin17°

$\sf{ \longrightarrow \: \: \dfrac{{cos}^{2}{27}^{\circ} + {sin}^{2}{27}^{\circ}}{{cos}^{2}{17}^{\circ} + {sin}^{2}{17}^{\circ}}}$

By using the identity [cos² A + sin² A = 1],

$\sf{ \longrightarrow \: \: \dfrac{1}{1}}$

$\sf{ \longrightarrow \: \: 1}$

Hence,

$\sf{\dfrac{{sin}^{2}{63}^{\circ} + {sin}^{2}{27}^{\circ}}{{cos}^{2}{17}^{\circ} + {cos}^{2}{73}^{\circ}} = 1}$