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sin⁡A/csc⁡A−cot⁡A=1+cos⁡A\sin A / \csc A - \cot A = 1+\cos A

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Find derivatives using the quotient rule IIright chevron icon

Full solution

Q. sin⁡A/csc⁡A−cot⁡A=1+cos⁡A\sin A / \csc A - \cot A = 1+\cos A
  1. Replace with reciprocals: Replace csc⁡A\csc A with 1sin⁡A\frac{1}{\sin A} and cot⁡A\cot A with cos⁡Asin⁡A\frac{\cos A}{\sin A}.\newlinesin⁡A/(1sin⁡A)−(cos⁡Asin⁡A)=1+cos⁡A\sin A / \left(\frac{1}{\sin A}\right) - \left(\frac{\cos A}{\sin A}\right) = 1 + \cos A
  2. Simplify by multiplying and subtracting: Simplify the expression by multiplying sin⁡A\sin A with 1sin⁡A\frac{1}{\sin A} and subtracting cos⁡Asin⁡A\frac{\cos A}{\sin A}.(sin⁡A⋅sin⁡A)sin⁡A−cos⁡Asin⁡A=1+cos⁡A\frac{(\sin A \cdot \sin A)}{\sin A} - \frac{\cos A}{\sin A} = 1 + \cos A
  3. Cancel out sin A: Cancel out the sin⁡A\sin A in the numerator and denominator in the first term.1−cos⁡Asin⁡A=1+cos⁡A1 - \frac{\cos A}{\sin A} = 1 + \cos A
  4. Replace with cot⁡A\cot A: Replace cos⁡Asin⁡A\frac{\cos A}{\sin A} with cot⁡A\cot A.\newline1−cot⁡A=1+cos⁡A1 - \cot A = 1 + \cos A

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