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If sin A=(11)/(61) and cos B=(20)/(29) and angles A and B are in Quadrant I, find the value of tan(A-B). Answer:

If sin⁡A=1161 \sin A=\frac{11}{61} and cos⁡B=2029 \cos B=\frac{20}{29} and angles A and B are in Quadrant I, find the value of tan⁡(A−B) \tan (A-B) .\newlineAnswer:

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Q. If sin⁡A=1161 \sin A=\frac{11}{61} and cos⁡B=2029 \cos B=\frac{20}{29} and angles A and B are in Quadrant I, find the value of tan⁡(A−B) \tan (A-B) .\newlineAnswer:
  1. Use Pythagorean identity: Use the Pythagorean identity to find cos⁡(A)\cos(A) and sin⁡(B)\sin(B). Since sin⁡A=1161\sin A = \frac{11}{61}, we can find cos⁡A\cos A using the identity sin⁡2A+cos⁡2A=1\sin^2 A + \cos^2 A = 1. cos⁡2A=1−sin⁡2A\cos^2 A = 1 - \sin^2 A cos⁡2A=1−(1161)2\cos^2 A = 1 - \left(\frac{11}{61}\right)^2 cos⁡2A=1−1213721\cos^2 A = 1 - \frac{121}{3721} cos⁡2A=37213721−1213721\cos^2 A = \frac{3721}{3721} - \frac{121}{3721} cos⁡2A=36003721\cos^2 A = \frac{3600}{3721} sin⁡(B)\sin(B)00 sin⁡(B)\sin(B)11

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