Question

3+cot80 degree cot20 degree/cot70degree+cot20 degree
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Answer 1

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Answer 2

Answer:

Step-by-step explanation:

3+cot80∘cot20∘cot80∘+cot20∘

=3+(cos80∘sin80∘)(cos20∘sin20∘)(cos80∘sin80∘)+(cos20∘sin20∘)

=3sin80∘sin20∘+cos80∘cos20∘sin20∘cos80∘+sin80∘cos20∘

=2sin80∘sin20∘+cos(80∘−20∘)sin(20∘+80∘)

=cos60∘−cos100∘+cos60∘sin100∘

=2cos60∘−cos100∘sin100∘

=2(12)−cos100∘sin100∘

=1−cos100∘sin100∘

=2sin250∘2sin50∘cos50∘

=sin50∘cos50∘

=tan50∘