Question 45

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 - (B)

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