Question

(sin5-sin15+sin25-sin35)/(cos5-cos15-cos25+cos35) =cot10​

Answer 1

Explanation:

(sin5-sin15+sin25-sin 35)/(cos 5-cos 15+cos 25 +cos 35)
`=(-(sin 35-sin 5)+(sin 25-sin 15))/((cos 35+cos 5)-(cos 25+cos 15)) \\`

`=(-2 cos (35+5)/(2)sin (35-5)/(2)+2 cos (25+15)/(2) sin (25-15)/(2) )/(2cos (35+5)/(2)cos (35-5)/(2)-2cos (25+15)/(2) cos (25-15)/(2) )`

`=(-cos 20 sin 15+cos 20 sin 5)/(cos 20 cos 15-cos 20 cos 5) \\`

`=(- cos 20(sin 15-sin 5))/(cos 20(cos 15-cos 5))`

`=(-(sin 15-sin 5))/(cos 15-cos 5)) \\=(-2cos (15+5)/(2)sin (15-5)/(2) )/(-2 sin (15+5)/(2)sin (15-5)/(2) ) } }`

`=(cos 10 sin 5)/(sin 10 sin 5)`

`=(cos 10)/(sin 10)`

=cot 10