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3 years ago

Verify the identity secx-secx sin^2x=cosx

1 answer:

6 0

Hello :
* secx = 1/cosx
cos²x+sin²x= 1
**sin²x = 1-cos²x
by (*) :
secx-secx sin²x=(1/cosx) -(1/cosx) sin²x
= (1/cosx)(1- sin²x)....factory :(1/cosx)
by(**)
secx-secx sin²x = (1/cosx)cos²x
secx-secx sin²x = cosx ...( simplify by : cosx)

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Solve: 12^x2+5x-4 =12^2x+6

lyudmila [28]

Answer:

x=2, x=-5

Step-by-step explanation:

to work more comfortably, the first thing we need to do is work the equation linearly, for that we take advantage of the property of logarithms that tells me that $log(a^{b})=b*log(a)$

in this way, the equation remains as:

$log(12^{x^{2} +5x-4 } )=log(12^{5x+6} ) \\ (x^{2} +5x-4 )*log(12)=(5x+6) *log(12)\\x^{2} +5x-4 = 5x+6$

Now we clear the equation so that it is of the form $ax^{2} +bx+c=0$

$x^{2} +5x-2x=6+4\\ x^{2} +3x-10=0$

finally, we apply the equation to solve second degree equations

$x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}$

$x = \frac{-3 \pm \sqrt {3^2-4*1*(-10)}}{2*1}\\ x = \frac{-3 \pm \sqrt {9+40}}{2}\\ x = \frac{-3 \pm 7}{2}$

x=2 and x=-5

Done

5 0

4 years ago

2.) Fill in the blank.

Montano1993 [528]

Answer:

E.) 1

Step-by-step explanation:

Firstly we will solve for L.H.S.

L.H.S. = $Csc^2\theta$

Since we know that $Csc^2\theta$ is the inverse of $Sin^2\theta$ .

So we can say that;

$csc^2\theta=\frac{1}{sin^2\theta}$

Now For R.H.S.

$Cot^2\theta+1$

Since we can rewrite $cot^2\theta$ as $\frac{cos^2\theta}{sin^2\theta}$ .

Now we can say that the R.H.S. is;

$\frac{cos^2\theta}{sin^2\theta}+1$

Now we add the fraction and get;

$\frac{cos^2\theta+sin^2\theta}{sin^2\theta}$

Now according to trigonometric identity;

$cos^2\theta+sin^2\theta=1$

So, $\frac{cos^2\theta+sin^2\theta}{sin^2\theta}=\frac{1}{sin^2\theta}$

Here,

$csc^2\theta=\frac{1}{sin^2\theta}$ and $Cot^2\theta+1$ = $\frac{1}{sin^2\theta}$ <em> </em>

L.H.S. = R.H.S.

Hence $csc^2\theta=cot^2\theta+1$

4 0

3 years ago

A health club manager wants to determine whether the members would prefer a new sauna or a new steam room. The club surveys 50 o

Arlecino [84]

Answer:

The population is all 600 members of the health club

Explanation:

50 members were chosen out of all 600 members thereby telling us that the sample of the study/survey is 50 members while the population is all 600 members. A sample represents the population and is collected from the population to make it less tedious to study and make conclusions on the population. For example, given that the population of a study are individuals or objects of common characteristics, 50 members tell the needed story and relays the characteristics and/or definition of the whole population, thereby forming a basis to make a conclusion on the population.

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3 years ago

|60| ___ |-60| > = < what is the answer

Nataly_w [17]

Answer: =

Step-by-step explanation:

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4 years ago

Estimate 660 divided by 7.

erik [133]

Answer:

660/ 70

Estimate of 94

Hope this helps

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4 years ago

Read 2 more answers