simplify sinAcosAtanA+2sinAcos^3A/sin2A

asked by guest
on Mar 31, 2025 at 2:24 pm



You asked:

Simplify the expression: sin⁡(A)cos⁡(A)tan⁡(A)+2sin⁡(A)⋅cos⁡(A)3sin⁡(2A)\sin\left( A \right) \cos\left( A \right) \tan\left( A \right) + \frac{2 \sin\left( A \right) \cdot {\cos\left( A \right)}^{3}}{\sin\left( 2 A \right)}

MathBot Answer:

Simplified:

sin⁡(A)cos⁡(A)tan⁡(A)+2sin⁡(A)⋅cos⁡(A)3sin⁡(2A)=sin⁡(2A)tan⁡(A)2+cos⁡(2A)2+12 \sin\left( A \right) \cos\left( A \right) \tan\left( A \right) + \frac{2 \sin\left( A \right) \cdot {\cos\left( A \right)}^{3}}{\sin\left( 2 A \right)} = \frac{\sin{\left(2 A \right)} \tan{\left(A \right)}}{2} + \frac{\cos{\left(2 A \right)}}{2} + \frac{1}{2}

Factored:

sin⁡(A)cos⁡(A)tan⁡(A)+2sin⁡(A)⋅cos⁡(A)3sin⁡(2A)=(sin⁡(2A)tan⁡(A)+2cos⁡2(A))sin⁡(A)cos⁡(A)sin⁡(2A) \sin\left( A \right) \cos\left( A \right) \tan\left( A \right) + \frac{2 \sin\left( A \right) \cdot {\cos\left( A \right)}^{3}}{\sin\left( 2 A \right)} = \frac{\left(\sin{\left(2 A \right)} \tan{\left(A \right)} + 2 \cos^{2}{\left(A \right)}\right) \sin{\left(A \right)} \cos{\left(A \right)}}{\sin{\left(2 A \right)}}


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