Question

Evaluate sin80°/cos10°+sin 59°.sec31°

Answer 1

sin(90-teta)=cos teta,sin80=cos10,cos10/cos/10=1.sec(90-teta)=cosec teta,sec31=cosec59,sin teta=1/sin teta, therefore cosec59=1/sin59.sin59×1/sin59=1.therefore,1+1=2

Answer 2

$\frac{ \sin(80) }{ \cos(10) } + \sin(59) . \sec(31)$

$\frac{ \sin(80) }{ \cos(90 - 10) } + \frac{ \sin(59) }{ \cos(31) }$

$\frac{ \sin(80) }{ \sin(80) } + \frac{ \sin(59) }{ \sin(90 - 31) }$

$\frac{ \sin(80) }{ \sin(80) } + \frac{ \sin(59) }{ \sin(59) }$

$1 + 1 = 2$