Question

If tana = 3/4 and cosb = 7/25, find the value of tan(a-b).

a) -23/61
b) -5/33
c) 1/3
d) 33/5

Answer 1

The value of tan(a-b) is found to be -33/5 by using trigonometric identities and the given values for tana and cosb, which corresponds to option d).

Step-by-step explanation:

To find the value of tan(a-b) given that tana = 3/4 and cosb = 7/25, we can use the following trigonometric identities:

1. tan(a-b) = (tan a - tan b) / (1 + tan a * tan b)
2. To find tan b, we use the identity tan^2 b + 1 = 1/cos^2 b. Since we know cosb = 7/25, we can find sinb using sin^2 b + cos^2 b = 1.
3. Calculating the above, we get sinb = ±24/25. We take the positive value because typically angles are taken from the first quadrant where sine values are positive.
4. tan b = sinb/cosb = 24/7. Now we have both tan a and tan b.
5. Substituting into the formula for tan(a-b), we get tan(a-b) = (3/4 - 24/7) / (1 + (3/4 * 24/7)). After calculation, we find that tan(a-b) = -33/5.

Therefore, the value of tan(a-b) is -33/5, which corresponds to option d).