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
luda_lava [24]
3 years ago
11

Prove that sin3a-cos3a/sina+cosa=2sin2a-1

Mathematics
2 answers:
makvit [3.9K]3 years ago
8 0

Answer:

To prove : sin(3a)-cos(3a)/sin(a)+cos(a) = 2sin(2a)-1                                      

Step-by-step explanation:

\frac{\sin3a-\cos3a}{\sin a+\cos a}=2\sin 2a-1\\\cos3a=4\cos^{3}a-3\cos a\\\sin 3a=3\sin a-4\sin ^{3}a\\substituting the value, we get\\L.H.S= \frac{3\sin a-4\sin ^{3}a-[4\cos ^{3}a-3\cos a]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4(\sin ^{3}a+4\cos ^{3}a)}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(\cos ^{2}a+\sin ^{2}a-\sin a\cos a)]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4+4\sin a\cos a]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)(-1+4\sin a\cos a)}{\sin a+\cos a}\\-1+4\sin a\cos a\\-1+2\sin 2a\\2\sin 2a-1=R.H.S

Since, sin(2a)= 2sin(a)cos(a)

2sin(2a)= 4sin(a)cos(a)



Sloan [31]3 years ago
7 0

Answer:

\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1

Step-by-step explanation:

we are given

\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1

we can simplify left side and make it equal to right side

we can use trig identity

sin(3a)=3sin(a)-4sin^3(a)

cos(3a)=4cos^3(a)-3cos(a)

now, we can plug values

\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)}

now, we can simplify

\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)}

\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)}

\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)}

now, we can factor it

\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)}

\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)}

we can use trig identity

sin^2(a)+cos^2(a)=1

\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)}

we can cancel terms

=3-4(1-sin(a)cos(a))

now, we can simplify it further

=3-4+4sin(a)cos(a))

=-1+4sin(a)cos(a))

=4sin(a)cos(a)-1

=2\times 2sin(a)cos(a)-1

now, we can use trig identity

2sin(a)cos(a)=sin(2a)

we can replace it

=2sin(2a)-1

so,

\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1


You might be interested in
Is this the correct answer?
charle [14.2K]
Yes, it is right... you correctly distributed the negative, and combined like terms... great job!
6 0
3 years ago
for y=x^2-10 do the following . A) Sketch a graph of the equation. B) Identify the vertex. C)Compare the graph of y=f(x) to the
Andreas93 [3]
A ) A graph of the equation is in the attachment.
B ) The vertex ( 0, -10 )
C ) The graph of y = x² is translated for 10 units down.
Download docx
8 0
3 years ago
How to solve simliar triangles
8090 [49]

Answer:

there is a formula to solve simlar triangle

Step-by-step explanation:

Ratios and properties-similar figures -In depth.if two object have same shape they are called similar.When two figure are similar,The ratios of the length of their corresponding sides are equal.To determine if the triangle shown are similar,Compare their corresponding sides.

7 0
3 years ago
Confused on number 10. I put one solution, but I don’t know if it’s right. I got
egoroff_w [7]
It is no answer, because when you get 12x + 48 = 48 + 12x, they cancel each other out.
8 0
3 years ago
Which decimal is equivalent to
antiseptic1488 [7]

Answer:

4.75

Step-by-step explanation:

19 goes into 4 4 times, so we are left with 4 3/4. 3/4 is 0.75, so we have 4.75 as our answer.

8 0
3 years ago
Read 2 more answers
Other questions:
  • Prachi, the office manager at a private practice, identified several quantitative relationships surrounding a patient's visit an
    9·1 answer
  • If a bicycle cost $70.50 but it's on sale for 47% off how much is the discount what is the sale price
    9·1 answer
  • X/2 - y/3 = 3/2<br>X/3 + y/2 = 16/3
    14·1 answer
  • Please help I’m being timed
    11·1 answer
  • 6.perimeter of the given shape above is
    15·2 answers
  • Heeeeeeeeellllllllllllllpppppppppppppppp mmmmmmmmmmmeeeeeeeeeeeeeeeeeeeeeeeeee​
    10·2 answers
  • A blueprint of a house shows a
    14·1 answer
  • I need help on this question
    10·1 answer
  • Help me please 20 points and brainliest
    9·1 answer
  • The figure below shows a line graph and two shaded triangles that are similar:
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!