Question

2 cos 67°/ sin 23° - tan 40°/ cot 50° + cos 0°​

Answer 1

${ \tt{ \large \underline{question \colon}}}$

$evalute \\ { \rm{2 \: \dfrac{cos67 \degree}{sin23 \degree} - \dfrac{tan 40 \degree}{cot50 \degree} + cos 0 \degree }}$

${ \tt{ \large \underline{solution \colon}}}$

${ \rm{2 \: \dfrac{cos67 \degree}{sin23 \degree} - \dfrac{tan 40 \degree}{cot50 \degree} + cos 0 \degree }}$

${ \rm{ = 2 \: \dfrac{cos67 \degree}{sin(90 \degree - 23 \degree)} - \dfrac{tan 40 \degree}{cot(90 \degree - 50 \degree)} + cos 0 \degree }}$

${ \rm{ = 2 \: \dfrac{cos67 \degree}{cos67 \degree} - \dfrac{tan 40 \degree}{ tan 40 \degree} + cos 0 \degree }}$

${ \rm{ = 2 \: \dfrac{ \not cos67 \degree}{ \not cos67 \degree} - \dfrac{ \not tan 40 \degree}{ \not tan 40 \degree} + cos 0 \degree }}$

${ \rm{ = 2 + cos0 \degree}}$

${ \rm{ = 2 + 1 = 3}}$

${ \tt{so \: the \: answer \: is = 3}}$