If A + B = frac{pi}{4}, then (1 + tan A)(1 + | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given that $A + B = \frac{\pi}{4}.$Taking tangent on both sides,we get $	an(A + B) = 	an\left(\frac{\pi}{4}ight).$Using the formula $	an(A +

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Given that $A + B = \frac{\pi}{4}.$Taking tangent on both sides,we get $	an(A + B) = 	an\left(\frac{\pi}{4}ight).$Using the formula $	an(A + B) = \frac{	an A + 	an B}{1 - 	an A 	an B},$ we have $\frac{	an A + 	an B}{1 - 	an A 	an B} = 1.$This implies $	an A + 	an B = 1 - 	an A 	an B.$Rearranging the terms,we get $	an A + 	an B + 	an A 	an B = 1.$Now,consider the expression $(1 + 	an A)(1 + 	an B) = 1 + 	an B + 	an A + 	an A 	an B.$Substituting the value $	an A + 	an B + 	an A 	an B = 1$ into the expression,we get $1 + 1 = 2.$Thus,$(1 + 	an A)(1 + 	an B) = 2.$

If $A + B = \frac{\pi}{4},$ then $(1 + \tan A)(1 + \tan B) = $

Similar Questions

$\cos \alpha \sin (\beta-\gamma) + \cos \beta \sin (\gamma-\alpha) + \cos \gamma \sin (\alpha-\beta)$ is equal to

Prove that $\sin^{2} 6x - \sin^{2} 4x = \sin 2x \sin 10x$.

The value of $\cos \left(\frac{7 \pi}{12}\right)$ is

If $2 \sin \left(\theta+\frac{\pi}{3}\right)=\cos \left(\theta-\frac{\pi}{6}\right)$,then $\tan \theta=$

If $\tan A = \frac{5}{6}$ and $\tan B = \frac{1}{11}$,then $A + B = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module