All categories

3 years ago

If a + b equal to pi by 4 then prove that 1 + cot a into 1 + cot B equal to 2 into cot a into cot b

Mathematics

1 answer:

o-na [289]3 years ago

4 0

Answer:

(cotA − 1) (cotB − 1) = 2

Step-by-step explanation:

A+B= π/4 = 180°/4 = 45°

A+B=45°

∴ cot(A+B)=cot45°

∴ cotBcotA−1 / (cotB+cotA) = 1

⇒cotB + cotA = cotBcotA = 1

⇒cotB + cotA − cotBcotA + 1 = 0

⇒cotBcotA − cotB − cotA − 1 = 0

⇒cotBcotA − cotB − cotA − 1 + 2 = 0+2

⇒cotBcotA − cotB − cotA + 1 = 2

⇒cotB(cotA − 1) (cotA − 1) = 2

⇒(cotA − 1) (cotB − 1) = 2

Proved

You might be interested in

3V3 х 60° Find the values of x and y. Write your answers in simplest form. X= y=

Alex787 [66]

Answer:

X=3

y=6

Step-by-step explanation:

$tan60=\sqrt{3}=\frac{3\sqrt{3} }{x} \\\\x=3$

-----------

$sin60=\frac{\sqrt{3} }{2} =\frac{3\sqrt{3} }{y} \\\\y=6$

hope it helps...

have a great day!!

6 0

3 years ago

Which of the following Triangle cases cannot be solved, using either the law of cosines or law of sines

hodyreva [135]

The answer is D. You cannot use aaa

8 0

3 years ago

Read 2 more answers

Given z1 = 1+i and z2 = 2+3i.

Margaret [11]

Answer:

(a) $w=2+5i-6=-4+5i$

Multiplicative inverse of w will be $\frac{1}{-4+5i}$

(B) As w is same as the product of $z_1\ and\ z_2$

So there multiplicative inverse will also be same

Step-by-step explanation:

We have given two complex numbers

$z_1=1+i$ and $z_2=3+2i$

(a) First we have to find $w=z_1z_2$

So $w=(1+i)(2+3i)=2+3i+2i+6i^2=2+5i+6i^2$

As we know that $i^2=-1$

So $w=2+5i-6=-4+5i$

Multiplicative inverse :

It is that number when multiply with the number which we have have to find the multiplicative inverse gives result as 1

So multiplicative inverse of w will be $\frac{1}{-4+5i}$

Because when we multiply $-4+5i$ with $\frac{1}{-4+5i}$ it gives result as 1

(b) As w is same as the product of $z_1\ and\ z_2$

So there multiplicative inverse will also be same

4 0

3 years ago

Approximate square root of 83 to to the nearest integer.

frez [133]

Answer:

9.1

Step-by-step explanation:

3 0

3 years ago

Select all that apply: the quotient of 0.04 and g

BaLLatris [955]

Answer:

A, B, C, and F is your possible answers

The quotient of means to divide so it could be any symbol and they could switch places when dividing.

5 0

3 years ago

If a + b equal to pi by 4 then prove that 1 + cot a into 1 + cot B equal to 2 into cot a into cot b​

If a + b equal to pi by 4 then prove that 1 + cot a into 1 + cot B equal to 2 into cot a into cot b