Calculus/maths

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Question
Good day

can u help me to prove that:sin A/1+cosA +cot A =cosec A

Answer
Hi Joel,
You can start by simplifying sinA/(1 + cosA). Multiply top and bottom by 1 - cosA and you'll have;
sinA/(1 + cosA) = sinA . (1 - cosA) / (1 + cosA) . (1 - cosA)
= sinA . (1 - cosA) / (1 - cosČA)
= sinA . (1 - cosA) / sinČA
= (1 - cosA) / sinA
= (1/sinA) - (cosA/sinA)
= cosecA - cotA
Therefore,
sinA/(1 + cosA) + cotA = cosecA - cotA + cotA
= cosecA

Hope its clear enough.
Regards

Calculus

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