If A + B = 4 , then (1 + A)(1 + B) = - Vidyadip

MCQ

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

A
$1$
✓
$2$
C
$\infty $
D
$-2$

✓

Answer

Correct option: B.

$2$

b
(b) Given that $A + B = \frac{\pi }{4}\,$

$\Rightarrow \,\tan \,(A + B) = \tan \,\frac{\pi }{4}$

$ \Rightarrow \,\,\frac{{\tan A + \tan B}}{{1 - \tan A\,\tan B}} = 1$

$ \Rightarrow \,\,\tan A + \tan B + \tan A\,\tan B = 1$

$ \Rightarrow \,\,(1 + \tan A)\,(1 + \tan B) = 2$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $m\tan (\theta - 30^\circ ) = n\tan (\theta + 120^\circ ),$ then $\frac{{m + n}}{{m - n}} = $

The chord $ PQ $ of the rectangular hyperbola $xy = a^2$ meets the axis of $x$ at $A ; C $ is the mid point of $ PQ\ \& 'O' $ is the origin. Then the $ \Delta ACO$ is :

Let $\ln x$ denote the logarithm of $x$ with respect to the base $e$. Let $S \subset R$ be the set of all points where the function $\ln \left(x^2-1\right)$ is well-defined. Then, the number of functions $f: S \rightarrow R$ that are differentiable, satisfy $f^{\prime}(x)=\ln \left(x^2-1\right)$ for all $x \in S$ and $f(2)=0$, is

If a variable line drawn through the point of intersection of straight lines $\frac{x}{\alpha } + \frac{y}{\beta } = 1$and $\frac{x}{\beta } + \frac{y}{\alpha } = 1$ meets the coordinate axes in $A$ and $B$, then the locus of the mid point of $AB$ is

If the roots of equation $5{x^2} - 7x + k = 0$ are reciprocal to each other, then value of $k$ is

Let $\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \quad \vec{b}=2 \hat{i}+3 \hat{j}-5 \hat{k} \quad$ and $\overrightarrow{\mathrm{c}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}$ be three vectors. Let $\overrightarrow{\mathrm{r}}$ be a unit vector along $\vec{b}+\vec{c}$. If $\vec{r} . \vec{a}=3$, then $3 \lambda$ is equal to :

On any given arc of positive length on the unit circle $|z|=1$ in the complex plane.

If $A = {\sin ^2}\theta + {\cos ^4}\theta ,$ then for all real values of $\theta$

The maximum value of ${\rm{cos}}{\alpha _1}.{\rm{cos}}{\alpha _2}........{\rm{cos}}{\alpha _n},$ under the restrictions $0 \le {\alpha _1},\,{\alpha _2},.......,\,{\alpha _n} \le \frac{\pi }{2}$ and ${\rm{cot}}{\alpha _1}.{\rm{cot}}{\alpha _2}....{\rm{cot}}{\alpha _n} = 1$ is

The diagonal passing through origin of a quadrilateral formed by $x = 0,\;y = 0,\;x + y = 1$ and $6x + y = 3,$ is