Question

please answer this cos80 /sin10+cos59cosec31

Answer 1

cos80/sin(90-80)+cos59/sin31
cos80/cos80 + cos59/sin(90-59)
1 + cos59/cos59
1+1
=w
2

Answer 2

$\bold{ \color{green} \mid \mid { \underline {\underline \red{ \star \: required \: answer \star \: }}}} \green{ \mid \mid}$

$\huge \bold{ \underline { \underline {we \: have : }}}$

$\bold{ \frac{ \cos80 \degree }{ \sin10 \degree } + \cos59 \degree \cosec 31 \degree }$

$\\ \\ \bold {\implies \frac{\sin(90 \degree - 80 \degree)}{ \sin10 \degree } + \: \sin(90 \degree - 59 \degree) \times \cosec31 \degree }$

$\bold{\implies \frac{ \sin10 \degree }{ \sin10 \degree} + \sin30 \degree \times \cosec31 \degree}$

$\bold{\implies1 + \frac{1}{ \cosec31 \degree} \times \cosec31 \degree}$

$\bold{\implies1 + 1 = 2}$

$hence</strong><strong>,</strong><strong>$

$\bold{{ \frac{ \cos80 \degree }{ \sin10 \degree } + \cos59 \degree \cosec 31 \degree } = 2}$