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
Alex777 [14]
3 years ago
7

Verify cot x sec^4x=cotx +2tanx +tan^3x

Mathematics
1 answer:
Tanzania [10]3 years ago
3 0

Answer:

See explanation

Step-by-step explanation:

We want to verify that:

\cot(x)  \:  { \sec}^{4} x =  \cot(x) + 2 \tan(x)   +  { \tan}^{3} x

Verifying from left, we have

\cot(x)  \:  { \sec}^{4} x  = \cot(x)  \: ( 1 +  { \tan}^{2} x )^{2}

Expand the perfect square in the right:

\cot(x)  \:  { \sec}^{4} x  = \cot(x)  \: ( 1 +  { 2\tan}^{2} x  + { \tan}^{4} x)

We expand to get:

\cot(x)  \:  { \sec}^{4} x  = \cot(x)  \:   +  \cot(x){ 2\tan}^{2} x  +\cot(x) { \tan}^{4} x

We simplify to get:

\cot(x)  \:  { \sec}^{4} x  = \cot(x)  \:   +  2 \frac{ \cos(x) }{\sin(x) ) }  \times  \frac{{ \sin}^{2} x}{{ \cos}^{2} x}   +\frac{ \cos(x) }{\sin(x) ) }  \times  \frac{{ \sin}^{4} x}{{ \cos}^{4} x}

Cancel common factors:

\cot(x)  \:  { \sec}^{4} x  = \cot(x)  \:   +  2 \frac{{ \sin}x}{{ \cos}x}   +\frac{{ \sin}^{3} x}{{ \cos}^{3} x}

This finally gives:

\cot(x)  \:  { \sec}^{4} x =  \cot(x) + 2 \tan(x)   +  { \tan}^{3} x

You might be interested in
4. There are seven days in a week. How many days are there in 16 weeks?
lesya692 [45]

Answer:

There are 112 days in 16 weeks

8 0
3 years ago
How to solve -5 + 13y = -7
zubka84 [21]

Answer:

y = -2/13

Step-by-step explanation:

-5 + 13y = -7

Add 5 to each side

-5+5 + 13y = -7+5

13y = -2

Divide by 13

13y/13 = -2/13

y = -2/13

5 0
3 years ago
Read 2 more answers
Can you pls help me solve this?​
soldi70 [24.7K]

Answer:

x=6. x=15

Step-by-step explanation:

13. x=6

16. x=15

7 0
3 years ago
Read 2 more answers
Five over seven plus blank over six equals fifty one over forty two
NISA [10]

Answer:

The blank is 3

Step-by-step explanation:

1 - Give the blank a variable

x = our blank

2 - Write it out

\frac{5}{7} + \frac{x}{6} = \frac{51}{42}

3 - Get the denominators equal

\frac{5}{7}(\frac{6}{6}) +\frac{x}{6}(\frac{7}{7}) = \frac{51}{42} \\\frac{30}{42}+\frac{7x}{42} = \frac{51}{42}

4 - Simplify

\frac{30+7x}{42} = \frac{51}{42} \\ \frac{30+7x}{42} = \frac{51}{42}

5 - Solve for the numerators

30+7x = 51

-30         -30

      7x = 21

        x = 3

6 0
3 years ago
Multiple choice question please answer it for me
timofeeve [1]
The answer is the second choice, or B; 240 ft^2.

You have to find the area of all four triangles and just add those all together. 

Two of the triangles have an area of 
5*16=80
Multiply that by two
80*2=160

The other two smaller triangles have an area of 
8*5=40
Multiply that by 2 also
40*2=80

Add 160+80 and the answer is 240.
6 0
3 years ago
Other questions:
  • Cameron classified -18/3 as real, rational, integer and a whole number and a whole number. Is he correct? why or why not?
    11·1 answer
  • Ryan sprinted 139 feet. How many yards did he sprint
    13·1 answer
  • One-third x + one-sixth y = 2. When x is 3, 1 x + StartFraction 3 Over 6 EndFraction y = 6. One-half x + three-fourths y = negat
    5·2 answers
  • Savannah had $13. She earned more money babysitting She now has at least $20.
    9·1 answer
  • What is the answer to the equation: 8+10
    13·2 answers
  • 1 + 4 x 3 + 1 x 5 = 66 this statement is false. How to use parentheses to fix this?
    8·1 answer
  • ;-; my last math question can someone please help meh!
    8·1 answer
  • 12 + 6 − 4 ÷ (2 + 5)
    5·1 answer
  • Solve for x: -2x+14=20
    14·2 answers
  • Question 2 of 10
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!