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Question

Transform the following expression

tanα+tanβcotα+cotβ+[cos(αβ)sec(α+β)+1]1.

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Solution

tanα+tanβcotα+cotβ+[cos(αβ)sec(α+β)+1]1
=tanα+tanβtanβ+tanαtanα.tanβ+1cos(αβ)cos(α+β)+1
=tanαtanβ+cos(α+β)cos(αβ)+cos(α+β)
=tanα.tanβ+cosαcosβsinαsinβ2cosαcosβ
=tanαtanβ+12tanαtanβ2
=12+tanαtanβ2=1+tanαtanβ2

1125370_887326_ans_388d976d70954c018d39662c046baeb1.jpeg

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