If A+B=45^ , then prove that : ( A-1)( B-1)=2 - Vidyadip

Question

If $A+B=45^{\circ}$, then prove that :
$(\cot A-1)(\cot B-1)=2$

✓

Answer

$\text {Given,}\quad A+B=45^{\circ} $
$\Rightarrow \quad \cot ( A + B )=\cot 45^{\circ}=1$
Now, $\quad \cot (A+B)=\frac{\cot A \cot B-1}{\cot A+\cot B}$
$\Rightarrow \quad 1=\frac{\cot A \cot B -1}{\cot A+\cot B }$
$\begin{array}{l}\Rightarrow \quad \cot A +\cot B =\cot A \cot B -1 \\ \Rightarrow \quad \cot A \cot B -\cot A -\cot B =1\end{array}$
Adding 1 on both sides :
$\begin{array}{l}\Rightarrow \quad 2=\cot A \cot B-\cot A-\cot B+1 \\\Rightarrow \quad 2=\cot A(\cot B-1)-1(\cot B-1) \\\Rightarrow \quad 2=(\cot A-1)(\cot B-1) \\\Rightarrow \quad(\cot A-1)(\cot B-1)=2\end{array}$

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 "2 Marks Questions" from PART - 1 CH - 3 Trigonometric Functions→PART - 1 CH - 3 Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10?

A die is thrown repeatedly until a six comes up. What is the sample space for this experiment.

If the function t which maps temperature in degree Celcius into temperature in degree Fahrenheit is defined by t(C) = $\frac{9C}{5}$+ 32, then find the value of C, when t(C) = 212.

Find the coefficient of:

x¹⁰ in the expansion of $\Big(2\text{x}^2-\frac{1}{\text{x}}\Big)^{20}.$

How many 2 digit even numbers can be formed from the digits 1, 2, 3, 4, 5 if the digits can be repeated?

Express the following complex numbers in the standard form a + ib:
$\frac{(1-\text{i})(1+\sqrt{3}\text{i})}{1-\text{i}}$

Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball.

Find the sun of first n odd natural numbers.

Find the derivative of function sin (x + a) (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers).

A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?