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
beks73 [17]
2 years ago
11

Sin(x+pi/4)-sin(x-pi/4)=1 solve the equation

Mathematics
1 answer:
evablogger [386]2 years ago
6 0
Sin(α+β)=sin(α)cos(β)+cos(α)sin(β)
sin(α-β)=sin(α)cos(β)-cos(α)sin(β)


sin(x+ \frac{ \pi }{4} )=sin(x)cos\frac{ \pi }{4} +cos(x)sin\frac{ \pi }{4}  \\ sin(x- \frac{ \pi }{4} )=sin(x)cos\frac{ \pi }{4} -cos(x)sin\frac{ \pi }{4}  \\ \\   \\sin(x+ \frac{ \pi }{4} )-sin(x- \frac{ \pi }{4} ) =1 \\ sin(x)cos\frac{ \pi }{4} +cos(x)sin\frac{ \pi }{4}  -(sin(x)cos\frac{ \pi }{4} -cos(x)sin\frac{ \pi }{4}  )=1 \\  sin(x)cos\frac{ \pi }{4} +cos(x)sin\frac{ \pi }{4}  -sin(x)cos\frac{ \pi }{4} +cos(x)sin\frac{ \pi }{4}  =1 \\  cos(x)sin\frac{ \pi }{4} +cos(x)sin\frac{ \pi }{4}  =1 \\
2cos(x)sin\frac{ \pi }{4}  =1    \\ sin\frac{ \pi }{4} = \frac{ \sqrt{2} }{2}  \\ 2cos(x) \frac{ \sqrt{2} }{2}  =1 \\ 2 \cdot \frac{ \sqrt{2} }{2}cos(x)   =1 \\   \sqrt{2} cos(x)=1 \\
cos(x)= \frac{1}{ \sqrt{2} }  \\ x=\pm arccos \frac{1}{ \sqrt{2} }+2 \pi k , k \in Z \\ x=\pm \frac{ \pi }{4} +2 \pi k , k \in Z
You might be interested in
The formula P = 6s gives the formula for the perimeter of a regular hexagon with side length s. What is the perimeter of a regul
stellarik [79]
YOU NEED A BETTER SCHOOL
6 0
3 years ago
Can someone hep with this question please it seems like i can't get the answer correctly.ty!!
Mashcka [7]

Answer:

your answer will be 5

Step-by-step explanation:

hope it helps have a nice day/night ^_^

bye

4 0
3 years ago
HELP PICTURE IS SHOWN
Lynna [10]
Its A because my class is litterally studing that now

6 0
3 years ago
What will you spend altogether if you got a movie ticket for $5 and popcorn and a water bottle
solmaris [256]
If they are all 5 dollars then it will be $15
5 0
2 years ago
Read 2 more answers
What is the slope intercept form of -1/2 and 1, -1/2 being the slope??
nevsk [136]
The slope-intercept form of the equation of a straight line is y=mx+b, where m is the slope and b is the y-coordinate of the y-intercept.

If the given slope is -1/2, then this equation becomes y = (-1/2)x + b.

You do not say that b=1.

But if we let b=1, then the equation becomes y = (-1/2)x + 1.


7 0
3 years ago
Other questions:
  • Factorise completely (2x+1)^2 -(x-1)^2
    13·1 answer
  • Please Help ASAP and please show your work​
    9·1 answer
  • What is the surface area of a cone that has a slant height of 18.5 inches and a radius of 11 inches?
    13·2 answers
  • Help help help helpn
    11·1 answer
  • Gasoline costs $2.79 per gallon Is the number of gallons proportional to the total cost
    9·1 answer
  • Would it be easier to find the slope or the x - intercpet of the line described by y= 2x +3? explain
    11·2 answers
  • The perimeter of a rectangle can be found using the equation p=2l+2w where p is the perimeter l is the length and w is the width
    9·1 answer
  • Any help with an explanation would be appreciated!
    8·1 answer
  • What is the x-intercept of the graph of y = –|x – 2|?
    13·1 answer
  • Students in a large district's two high schools are offered a "Second Breakfast' program after their first-period class.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!