1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sveticcg [70]
3 years ago
14

Is anybody else here to help me ??​

Mathematics
1 answer:
Akimi4 [234]3 years ago
7 0

Answer:

\cot(x)+\cot(\frac{\pi}{2}-x)

\cot(x)+\tan(x)

\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}

\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})

\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})

\csc(x)[\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}]

\csc(x)[\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}]

\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}]

\csc(x)[\frac{1}{\cos(x)}]

\csc(x)[\sec(x)]

\csc(x)[\csc(\frac{\pi}{2}-x)]

\csc(x)\csc(\frac{\pi}{2}-x)

Step-by-step explanation:

I'm going to use x instead of \theta because it is less characters for me to type.

I'm going to start with the left hand side and see if I can turn it into the right hand side.

\cot(x)+\cot(\frac{\pi}{2}-x)

I'm going to use a cofunction identity for the 2nd term.

This is the identity: \tan(x)=\cot(\frac{\pi}{2}-x) I'm going to use there.

\cot(x)+\tan(x)

I'm going to rewrite this in terms of \sin(x) and \cos(x) because I prefer to work in those terms. My objective here is to some how write this sum as a product.

I'm going to first use these quotient identities: \frac{\cos(x)}{\sin(x)}=\cot(x) and \frac{\sin(x)}{\cos(x)}=\tan(x)

So we have:

\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}

I'm going to factor out \frac{1}{\sin(x)} because if I do that I will have the \csc(x) factor I see on the right by the reciprocal identity:

\csc(x)=\frac{1}{\sin(x)}

\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})

\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})

Now I need to somehow show right right factor of this is equal to the right factor of the right hand side.

That is, I need to show \cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)} is equal to \csc(\frac{\pi}{2}-x).

So since I want one term I'm going to write as a single fraction first:

\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)}

Find a common denominator which is \cos(x):

\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}

\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}

\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}

By  the Pythagorean Identity \cos^2(x)+\sin^2(x)=1 I can rewrite the top as 1:

\frac{1}{\cos(x)}

By the quotient identity \sec(x)=\frac{1}{\cos(x)}, I can rewrite this as:

\sec(x)

By the cofunction identity \sec(x)=\csc(x)=(\frac{\pi}{2}-x), we have the second factor of the right hand side:

\csc(\frac{\pi}{2}-x)

Let's just do it all together without all the words now:

\cot(x)+\cot(\frac{\pi}{2}-x)

\cot(x)+\tan(x)

\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}

\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})

\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})

\csc(x)[\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}]

\csc(x)[\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}]

\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}]

\csc(x)[\frac{1}{\cos(x)}]

\csc(x)[\sec(x)]

\csc(x)[\csc(\frac{\pi}{2}-x)]

\csc(x)\csc(\frac{\pi}{2}-x)

You might be interested in
Look at pic 10 pts will mark brainilest
telo118 [61]

Answer:

can we go with D. 54 ?

the height and length is 9 and 6

9x6= 54

7 0
2 years ago
Read 2 more answers
Grace was driving down a road and after 4 hours she had traveled 66 miles. At this speed, how many miles could Grace travel in 8
umka2103 [35]

Answer:

132 miles

Step-by-step explanation:

4 is half of 8 so you just have to multiple everything by 2 to get your answer

6 0
2 years ago
Read 2 more answers
How much cash did Vera receive?
Ber [7]

There is a box labeled * Less Cash Received in the deposit ticket. The number in this box would be the amount of cash Vera received.

The number in this box is 80.00.

Vera received $80.00

4 0
3 years ago
Read 2 more answers
I want to divid 18 divided by 5
user100 [1]

Answer:

The answer is 3.6

7 0
3 years ago
Read 2 more answers
For a daily airline flight between two cities, the number of pieces of checked luggage has a mean of 380 and a standard deviatio
Olegator [25]
<span>Since one standard deviation is 20 luggages, 3 standard deviations above the mean is 3*20=60 luggages above the mean of 380 luggages, so 60+380 gives the answer C, 440.</span>
3 0
3 years ago
Read 2 more answers
Other questions:
  • Let f(x) = x^2 +3x and g(x) =2x -1 (f+g)(3)
    13·1 answer
  • Write 0.87 as a fraction
    15·2 answers
  • Which choice shows the best estimate of the product 0.52×695 ?
    15·1 answer
  • I have a 2 in the tens place. when you add 18 to me, you get 39. what number am I ?
    12·1 answer
  • Does (-15, -691) make the equation y = -51x - 74 true?<br><br><br>​
    15·2 answers
  • Which is f(5) for the function -2xsquared + 2x -3
    5·1 answer
  • I need help pleaseee!!
    15·1 answer
  • Of 220 seventh-grade students, 25% earn the Community Service Award. How many students earn the award?
    14·2 answers
  • True or false: Two numbers are reciprocals of each other if they have different signs in front.
    10·2 answers
  • Is associative prperty holds good under subtraction over integer​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!