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

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

Question

(B) Given that $	heta + \phi = \frac{\pi}{4}$.Taking $	an$ on both sides, we get $	an(	heta + \phi) = 	an(\frac{\pi}{4}) = 1$.Using the formula $

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Given that $	heta + \phi = \frac{\pi}{4}$.Taking $	an$ on both sides, we get $	an(	heta + \phi) = 	an(\frac{\pi}{4}) = 1$.Using the formula $	an(	heta + \phi) = \frac{	an 	heta + 	an \phi}{1 - 	an 	heta 	an \phi} = 1$.This implies $	an 	heta + 	an \phi = 1 - 	an 	heta 	an \phi$, or $	an 	heta + 	an \phi + 	an 	heta 	an \phi = 1$.Now, consider the expression $(1 + 	an 	heta)(1 + 	an \phi) = 1 + 	an \phi + 	an 	heta + 	an 	heta 	an \phi$.Substituting the value from the previous step: $1 + (	an 	heta + 	an \phi + 	an 	heta 	an \phi) = 1 + 1 = 2$.

If $\theta+\phi=\frac{\pi}{4}$, then $(1+\tan \theta)(1+\tan \phi)$ is equal to

Similar Questions

Prove that: $2 \cos \frac{\pi}{13} \cos \frac{9 \pi}{13} + \cos \frac{3 \pi}{13} + \cos \frac{5 \pi}{13} = 0$

The value of $\cos 105^\circ + \sin 105^\circ$ is

Prove that $\frac{\sin x-\sin y}{\cos x+\cos y}=\tan \left(\frac{x-y}{2}\right)$

$\cos 48^{\circ} \cdot \cos 12^{\circ} = ?$

For $\alpha, \beta \in \left(0, \frac{\pi}{2}\right)$,let $3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta)$ and a real number $k$ be such that $\tan \alpha=k \tan \beta$. Then the value of $k$ is equal to :

Vedclass Test Series

Exam Paper Generator

Online Exam Module