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Sedbober [7]
2 years ago
15

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

Mathematics
1 answer:
OleMash [197]2 years ago
5 0

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

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