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3 years ago

Solve the inequality IxI < 5

Mathematics

1 answer:

Elodia [21]3 years ago

3 0

Answer:

the correct answer is the second one

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) f) 1 + cot²a = cosec²a

notsponge [240]

Answer:

It is an identity, proved below.

Step-by-step explanation:

I assume you want to prove the identity. There are several ways to prove the identity but here I will prove using one of method.

First, we have to know what cot and cosec are. They both are the reciprocal of sin (cosec) and tan (cot).

$\displaystyle \large{\cot x=\frac{1}{\tan x}}\\\displaystyle \large{\csc x=\frac{1}{\sin x}}$

csc is mostly written which is cosec, first we have to write in 1/tan and 1/sin form.

$\displaystyle \large{1+(\frac{1}{\tan x})^2=(\frac{1}{\sin x})^2}\\\displaystyle \large{1+\frac{1}{\tan^2x}=\frac{1}{\sin^2x}}$

Another identity is:

$\displaystyle \large{\tan x=\frac{\sin x}{\cos x}}$

Therefore:

$\displaystyle \large{1+\frac{1}{(\frac{\sin x}{\cos x})^2}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{1}{\frac{\sin^2x}{\cos^2x}}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}$

Now this is easier to prove because of same denominator, next step is to multiply 1 by sin^2x with denominator and numerator.

$\displaystyle \large{\frac{\sin^2x}{\sin^2x}+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}\\\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}$

Another identity:

$\displaystyle \large{\sin^2x+\cos^2x=1}$

Therefore:

$\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}\longrightarrow \boxed{ \frac{1}{\sin^2x}={\frac{1}{\sin^2x}}}$

Hence proved, this is proof by using identity helping to find the specific identity.

6 0

2 years ago

Please helppppppppppppp

STatiana [176]

Answer:

275 miles

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Determine if the three lengths given will be able to construct a triangle or not.

borishaifa [10]

Answer:

1) No

2) No

3) Yes

4) No

5) Yes

Step-by-step explanation:

All three sides must add with another to be greater than the last side (Not sure if that makes sense ._.)

5 0

2 years ago

Read 2 more answers

Molly is converting 2 yards to millimeters. will the number of millimeters be fewer than or greater than 2?

Maru [420]

<span>Greater than, because millimeters are smaller than yards. i had this question 2</span>

8 0

3 years ago

The Spanish club decides to sell school pins $1.50 each and T-shirts at $6.50 each for a fundraiser. They projects that they wil

Firdavs [7]

Ok so 1.5 is pins and 6.5 is t shirts so you multiply 1.5 x 20 and 6.5 x 5 so for pins= $30 and T-shirts= $32.50 and you times both those numbers by 3 so for pins you get $90 and T-shirts you get $97.50. Finally you add them and get $187.5 so the answer is $187.5 for the project.

5 0

3 years ago

Solve the inequality IxI < 5​

Solve the inequality IxI < 5