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
Ratling [72]
2 years ago
13

Prove that: (Sec A- cosec A)(1+ tan A+cot A) = tan A× sec A - cot A × cosec A

Mathematics
1 answer:
mash [69]2 years ago
3 0

Answer:

Step-by-step explanation:

(sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA

we take the LHS so here goes,

(sec A-cosecA)(1+tanA+cotA)=tanAsecA-cotAcosecA\\(\frac{1}{cosA} -\frac{1}{sinA})(1+\frac{sinA}{cosA}+\frac{cosA}{sinA})\\\\(\frac{sinA-cosA}{sinAcosA})(\frac{sinAcosA+sin^2A+cos^2A}{sinAcosA})\\

since , sin^2A+cos^2A=1

the identity becomes,

(\frac{sinA-cosA}{sinAcosA})(\frac{1+sinAcosA}{sinAcosA})\\\\(\frac{sinA+sin^2AcosA-cosA-cos^2AsinA}{sin^2Acos^2A})\\\\

now, we know,

sin^2A=1-cos^2A and cos^2A=1-sin^2A

the identity becomes,

(\frac{sinA+(1-cos^2A)cosA-cosA-(1-sin^2A)sinA}{sin^2Acos^2A} )\\\\

(\frac{sinA+cosA-cos^3A-cosA-sinA+sin^3A}{sin^2Acos^2A})

sin A and cos A cancel out it becomes zero

\frac{sin^3A-cos^3A}{sin^2Acos^2A} \\\\

Splitting the denominator the identity becomes

\frac{sin^3A}{sin^2Acos^2A}-\frac{cos^3A}{sin^2Acos^2A}  \\\\\frac{sinA}{cos^2A} - \frac{cosA}{sin^2A} \\\\\frac{sinA}{cosA}(\frac{1}{cosA})-\frac{cosA}{sinA}(\frac{1}{sinA})\\\\

Hence,

tanAsecA-cotAcosecA

You might be interested in
Which is the correct answer​
Sav [38]

Answer:

Option 3

Step-by-step explanation:

Using the order of operations, you will find out that 7 x 10^3 = 7,000, and 3 x 10^2 = 300. Dividing 7,000 by 300 will get you 23.333~, so 300 does go into 7,000 a little more than 20 times.

8 0
2 years ago
What else equals 42 and 30 for multiply
aev [14]

Answer:

1 times 42 and 6 times 7 for 42

1 times 0 and 5 times 6

(I did this question in school once)

7 0
2 years ago
Regroup hundreds as Tens:<br><br> 8 hundreds 9 tens =
Lilit [14]
89 tens because 8 x10 is 80 add the 9
89
7 0
3 years ago
​A cable company has a one time installation fee and then a monthly charge to use their service. The total cost of modeled by th
SpyIntel [72]

Answer:

130=monthly charge

119=one time installation fee

Step-by-step explanation:

119 is the y-intercept and in problems like these, it is always the one time fee. 130 is the monthly payment because it has an x, which could account for the number of months. For example , say six months passed, you could multiply 130 * 6 to get the monthly fee for six months. I hope that makes sense!

6 0
2 years ago
What is:<br> <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B4x%5E%7B2%7D%20-20x%2B25%20" id="TexFormula1" title=" \sqrt{4x^{2} -
Firdavs [7]

We are given :

\sqrt{4x^{2}-20x+25}

Step 1: factor the part inside square root

The function given inside square root is of quadratic form.

So let us try to factorise it using AC method.

Here A*C = 4*25 = 100

so we have to find factors of 100 that add up to give -20.

the two factors are -10 and -10.

Rewriting the function :

4x^{2} -20x+25

=4x^{2} -10x-10x+25

=2x(2x-5) - 5(2x-5)

=(2x-5)^{2}

Step 2:

Now we take square root of the factorised form

\sqrt{(2x-5)^2}

= 2x-5

Answer : (2x-5)

3 0
3 years ago
Other questions:
  • If 6 bottles of perfect water weigh a total of 4 kilograms, what is the weight of 9 bottles?
    7·2 answers
  • Which of the following matches the graph?<br><br> Y=3/4x<br> Y=1/4x<br> Y=1/3x<br> Y=4x<br> Y=4/3
    8·2 answers
  • Which function is an odd function?
    9·1 answer
  • A man bought a car for 15000GH cedis . He later sold it at a profit of 25% .What was his selling price.
    10·2 answers
  • 4/5 make this to a whole number
    6·2 answers
  • The sixth grade art students are making a mosaic using tiles in the shape of right triangles. Each tile has leg measures of 3 ce
    12·1 answer
  • Isaac and Paul shared some baseball cards in the ratio 2:5. If Paul gave 30 cards to Isaac, they would have the same number of c
    14·1 answer
  • Can someone please help me please?
    15·2 answers
  • A
    6·1 answer
  • What is the perimeter of a square who’s sides are ten units long?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!