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
konstantin123 [22]
3 years ago
9

4.

Mathematics
1 answer:
zubka84 [21]3 years ago
3 0

Answer:

See Explanation Below

Step-by-step explanation:

Given

(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.

Required

Prove

To start with; we open the bracket on the left hand side

(sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)

(sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)

(sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x

(sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x

Reorder

(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x

From trigonometry;

sin^2x + cos^2x = 1

So;

(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x

becomes

(sin x - cos x)^2 = 1 - 2sinx cos x

Also from trigonometry;

sec^2x - tan^2x = 1

So,  

(sin x - cos x)^2 = 1 - 2sinx cos x

becomes

(sin x - cos x)^2 = sec^2x - tan^2x  - 2sinx cos x

Proved

You might be interested in
In the coordinate plane, what is the length of the line segment that connects points at (5, 4) and (−3, −1) ? Enter your answer
stiks02 [169]
The distance between two points knowing theirs coordinates:

AB =√[(x₂-x₁)² +(y₂-y₁)²]; ===>A(5,-4) & B(-3,-1) Given
                                                A(x₁,y₁) & B(x₂,y₂)

AB =√[(-3-5))²+(-1-(-4)²] =√(73) = 8.381 ≈ 5.44 units
3 0
2 years ago
Which expression can be used to find the radius of a circle with a diameter of 90 inches?
rjkz [21]
The answer to this is C, 90/2
6 0
2 years ago
Read 2 more answers
7/11÷2/5=<br>A.1/11<br>B.22/35<br>C.5/6<br>D.35/22
Tamiku [17]
The answer's D. 35/22

Well i have to write 20 words so dont mind this part
7 0
3 years ago
Find area and circumference of the circle (12.) pls NO links
xxTIMURxx [149]

Answer:

The area is 452.39

The Circumference is 75.36

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Write an equation of each line in point-slope form. containing (2,1) and (3,4)
Leokris [45]

Answer:

y=3x-5

Step-by-step explanation:

This is the only line that will pass through these points.

7 0
2 years ago
Other questions:
  • A store is selling a black pair of shoes for $79.45 and a brown pair of shoes for $133.99. the black pair of shoes is marked up
    12·2 answers
  • ASAP WILL MARK BRAINLIEST<br> If UW = 6x - 35, find UW.
    12·2 answers
  • The area of a square is 32 more than its perimeter. find the length of a side.
    11·1 answer
  • Anybody got the answer to this
    14·2 answers
  • Simplify<br> 9 to the power of 2 <br> Over <br> 9 to the power of 7
    5·1 answer
  • What fraction of a gallon is a quart
    5·2 answers
  • Need help plz ASAP!!!
    11·1 answer
  • Hombres ilustres matemáticos en orden cronológico​
    5·1 answer
  • The Staten Island Skating Pavilion charges a $5 entrance fee and an hourly rate for for ice skating. The total cost for ice skat
    9·1 answer
  • Please help me out with this asap.​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!