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lilavasa [31]
3 years ago
15

Verify the identity. 1+tan x/sin x + cos x= sec x

Mathematics
1 answer:
lakkis [162]3 years ago
5 0

Step-by-step explanation:

Taking left hand side:

\frac{1+tan\ x}{sin\ x+cos\ x}\\=\frac{1+\frac{sin\ x}{cos\ x} }{sin\ x+cos\ x}\\=\frac{\frac{cos\ x+sin\ x}{cos\ x} }{sin\ x+cos\ x}\\=\frac{cos\ x+sin\ x}{cos\ x} * \frac{1}{sin\ x+cos\ x}\\=\frac{1}{cos\ x}

1/cos x is equal to sec x.

So,

\frac{1}{cos\ x} = sec\ x

Hence proved ..

You might be interested in
2, 6, 18, 54. 162,...
grigory [225]

9514 1404 393

Answer:

  \text{c. }f(n)=3f(n-1);f(1)=2

Step-by-step explanation:

The first term is 2, so part of the recursive definition is ...

  f(1) = 2

The common ratio is 6/2 = 3, so each term is 3 times the previous one. That part of the recursive definition is ...

  f(n) = 3·f(n -1)

These two parts of the definition match choice C.

3 0
2 years ago
Solve for g in the proportion.<br><br> 42/g = 14/10<br><br> g =
NeX [460]

Cross mutiply. 42*10= 420. 14*g= 14g

14g= 420

divide by 14 for both sides

14g/14= 420/14

g= 30

Check answer by using substitution method

42/30. Divide by 3 . 42/3= 14 , 30/3= 10

14/10 and 14/10 equal to each other by dividing 2.

14/2= 7 , 10/2= 5

7/5= 7/5

Answer: g= 30

6 0
2 years ago
Read 2 more answers
A regular pentagon has a perimeter of 5x+15 what is the length of one side
dsp73

Answer:

plz give full question

its just half

6 0
2 years ago
The sales of a particular brand of children’s athletic shoes rose from $6,900,000 to $7,400,000. Find the percent of increase in
Sidana [21]

Answer:  7.2%

Step-by-step explanation:

First find the difference between the amounts.

7,400, 000 - 6, 900,000 = 500, 000  

Now divide the obtain number by  the original number which is 6,900,000

500, 000/ 6,900,000 = 0.07246  

Multiply 0.07246 by 100 to convert it to a percent.

0.07246  = 7.2463..%  

Round it to the nearest tenth of a percent.

7.2463.. rounded to the nearest tenth is 7.2%

8 0
2 years ago
A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms
MissTica

Answer:

t = \frac{39.5-30.6}{\frac{6.6}{\sqrt{25}}}= 6.74

The degrees of freedom are given by:

df =n-1= 25-1=24

Now we can calculate the p value with the following probability:

p_v = 2*P(t_{24}>6.74)= 5.69x10^{-7}

And for this case since the p value is lower compared to the significance level \alpha=0.05 we can reject the null hypothesis and we can conclude that the true mean for this case is different from 30.6 at the significance level of 0.05

Step-by-step explanation:

For this case we have the following info given:

\bar X = 39.5 represent the sample mean

s =6.6 represent the sample deviation

\mu = 30.6 represent the reference value to test.

n = 25 represent the sample size selected

The statistic for this case is given by:

t =\frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}

And replacing we got:

t = \frac{39.5-30.6}{\frac{6.6}{\sqrt{25}}}= 6.74

The degrees of freedom are given by:

df =n-1= 25-1=24

Now we can calculate the p value with the following probability:

p_v = 2*P(t_{24}>6.74)= 5.69x10^{-7}

And for this case since the p value is lower compared to the significance level \alpha=0.05 we can reject the null hypothesis and we can conclude that the true mean for this case is different from 30.6 at the significance level of 0.05

3 0
3 years ago
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