If cos A=(21)/(29) and tan B=(9)/(40) and angles A and B are in Quadrant I, find the value of tan(A-B). Answer:

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If  cos A=(21)/(29) and  tan B=(9)/(40) and angles A and B are in Quadrant I, find the value of  tan(A-B). Answer:

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Find tan A: Use the formula for tan(A-B), which is tan(A-B) = (tan A - tan B) / (1 + tan A * tan B). First, we need to find tan A. Since we know cos A = 21/29 and A is in Quadrant I, we can find sin A using the Pythagorean identity sin^2 A + cos^2 A = 1. sin^2 A = 1 - cos^2 A sin^2 A = 1 - (21/29)^2 sin^2 A = 1 - 441/841 sin^2 A = 841/841 - 441/841 sin^2 A = 400/841 sin A = √(400/841) sin A = 20/29 Now, tan A = sin A / cos A tan A = (20/29) / (21/29) tan A = 20/21Substitute values into formula: Now we have tan A = 20/21 and tan B = 9/40. We can substitute these values into the tan(A-B) formula. tan(A-B) = (tan A - tan B) / (1 + tan A * tan B) tan(A-B) = (20/21 - 9/40) / (1 + (20/21 * 9/40))Simplify numerator and denominator: Simplify the numerator and the denominator separately. For the numerator: tan A - tan B = 20/21 - 9/40 To subtract these fractions, find a common denominator, which is 21*40 = 840. (20/21 - 9/40) = (20*40)/(21*40) - (9*21)/(40*21) (20/21 - 9/40) = (800/840) - (189/840) (20/21 - 9/40) = (800 - 189)/840 (20/21 - 9/40) = 611/840 For the denominator: 1 + tan A * tan B = 1 + (20/21 * 9/40) 1 + tan A * tan B = 1 + (180/840) 1 + tan A * tan B = 840/840 + 180/840 1 + tan A * tan B = 1020/840Divide to find tan(A-B): Now, divide the numerator by the denominator to find tan(A-B). tan(A-B) = (611/840) / (1020/840) When dividing by a fraction, multiply by the reciprocal of the divisor. tan(A-B) = (611/840) * (840/1020) Simplify by canceling out the common factor of 840. tan(A-B) = 611/1020 Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1. tan(A-B) = 611/1020

If $\cos A=\frac{21}{29}$ and $\tan B=\frac{9}{40}$ and angles A and B are in Quadrant I, find the value of $\tan (A-B)$ . $\newline$ Answer:

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If cos⁡A=2129 \cos A=\frac{21}{29} cosA=2921​ and tan⁡B=940 \tan B=\frac{9}{40} tanB=409​ and angles A and B are in Quadrant I, find the value of tan⁡(A−B) \tan (A-B) tan(A−B).\newlineAnswer:

If $\cos A=\frac{21}{29}$ and $\tan B=\frac{9}{40}$ and angles A and B are in Quadrant I, find the value of $\tan (A-B)$ . $\newline$ Answer: