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

MCQ

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

A
2
B
$0$
C
1
D
3

✓

Answer

(a) 2
Explanation: $\tan (A-B)=\tan \frac{\pi}{4}$
$\Rightarrow \frac{\tan A-\tan B}{1+\tan A \tan B}=1$
$\Rightarrow \tan A=\tan B=1+\tan A \tan B \ldots$ (i)
Now,
$\begin{array}{l}(1+\tan A)(1-\tan B)=1+\tan A=\tan B=\tan A \tan B \\ =1+1+\tan A \tan B=\tan A \tan B \text { (Using eq. (i)) } \\ =2\end{array}$

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

More "M.C.Q (1 Marks)" from Model Paper 2→Model Paper 2 — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Six boys and six girls sit in a row randomly. The probability that all girls sit together is

$\frac{1}{122}$
$\frac{1}{112}$
$\frac{1}{102}$
$\frac{1}{132}$

A pendulum swings through an angle of $42^{\circ}$ in describing an arc of length 55 cm . The length of the pendulum is

If $A$ and $B$ are two sets, then $A \cap(A \cup B)$ equals

Choose the correct answers from the given four option:
Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively,

The negation of the statement.

“72 is divisible by 2 and 3” is.

72 is not divisible by 2 or 72 is not divisible by 3.
72 is not divisible by 2 and 72 is not divisible by 3.
72 is divisible by 2 and 72 is not divisible by 3.
72 is not divisible by 2 and 72 is divisible by 3.

If ${^\text{n}}\text{C}_{\text{12}}={^\text{n}}\text{C}_{\text{8}},$ is then n:

20
12
6
30

For an increasing A.P. a1, a2, a3..... an, if a1, a3, a5 = – 12 and a1. a3. a5 = 80, then which of the following is/are true?

Six boys and six girls sit along a line alternately in x ways and along a circle (again alternatively in y ways), then:

If f(x) = ex and g(x) = loge x then the value of fog(1) is:

The products of any r consecutive natural numbers is always divisible by: