Question

Cos10_sin10÷cos10+sin10=tan35

Answer 1

LHS = (cos10 - sin10) /(cos10+sin10)
we know,
cos(90-A) = sinA use this here,

= {cos10 - cos(90-10)}/{cos10+cos(90-10)}
= (cos10-cos80)/(cos10+cos80)

now, use the concept ,
cosC - cosD = 2sin(C+D)/2.sin(D-C)/2
cosC + cosD = 2cos(C+D)/2.cos(C-D)/2

= {2sin(10+80)/2.sin(80-10)/2}/{2cos(10+80)/2.cos(80-10)/2}
= (2sin45°.sin35°)/(2cos45°.cos35°)
=sin35°/cos35°
= tan35° = RHS