Question

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

Answer 1

Answer:

Step-by-step explanation:

(sin5-sin15+sin25-sin 35)/(cos 5-cos 15+cos 25 +cos 35)$=\frac{-(sin 35-sin 5)+(sin 25-sin 15)}{(cos 35+cos 5)-(cos 25+cos 15)}$

$=\frac{-2 cos \frac{35+5}{2}sin \frac{35-5}{2}+2 cos \frac{25+15}{2} sin \frac{25-15}{2} }{2cos \frac{35+5}{2}cos \frac{35-5}{2}-2cos \frac{25+15}{2} cos \frac{25-15}{2} }$

$=\frac{-cos 20 sin 15+cos 20 sin 5}{cos 20 cos 15-cos 20 cos 5}$

$=\frac{- cos 20(sin 15-sin 5)}{cos 20(cos 15-cos 5)}$

$=\frac{-(sin 15-sin 5)}{cos 15-cos 5)} \\=\frac{-2cos \frac{15+5}{2}sin \frac{15-5}{2} }{-2 sin \frac{15+5}{2}sin \frac{15-5}{2} } } }$

$=\frac{cos 10 sin 5}{sin 10 sin 5}$

$=\frac{cos 10}{sin 10}$

=cot 10