Question 91

If tan(A - B) = X, then the value of X is

Solution

Expression : tan(A - B) = X

= $$\frac{sin(A - B)}{cos(A - B)}$$

= $$\frac{sinAcosB-cosAsinB}{cosAcosB+sinAsinB}$$

Dividing both numerator and denominator by $$(cosAcosB)$$

= $$\frac{sinAcosB-cosAsinB}{cosAcosB}\div\frac{cosAcosB+sinAsinB}{cosAcosB}$$

= $$\frac{tanA-tanB}{1+tanAtanB}$$

=> Ans - (C)

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