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ozzi
3 years ago
15

Sin(x+y)-sin(x-y)/cos(x+y)+cos(x-y)=tany how do i verify this?

Mathematics
1 answer:
dsp733 years ago
7 0

Answer:

Step-by-step explanation:

Numerator

sin

x

cos

y

+

cos

x

sin

y

−

[

sin

x

cos

y

−

cos

x

sin

y

)

=

sin

x

cos

y

+

cos

x

sin

y

−

sin

x

cos

y

+

cos

x

sin

y

=

2

cos

x

sin

y

Denominator

cos

x

cos

y

−

sin

x

sin

y

+

cos

x

cos

y

+

sin

x

sin

y

=

cos

x

cos

y

−

sin

x

sin

y

+

cos

x

cos

y

+

sin

x

sin

y

=

2

cos

x

cos

y

---------------------------------------------------------------

left side can now be expressed as

2

cos

x

sin

y

2

cos

x

cos

y

=

2

cos

x

sin

y

2

cos

x

cos

y

=

sin

y

cos

y

and  

sin

y

cos

y

=

tan

y

=

right side hence proved

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Alja [10]
First we need to multiply to make the fractions have equal denominators so we can add/subtract.

math: 1/3 x 4/4=4/12
science: 1/4 x 3/3=3/12

Now we can find the time she spent on history (I assume this is what you are looking for)

Total time-math time<span>-science time=history time</span>
12/12-4/12-3/12
=5/12

Amy spent 5/12 of her time working on history.

8 0
2 years ago
Read 2 more answers
1.
ASHA 777 [7]

Answer:

Step-by-step explanation:

Vertex A of the triangle ABC when rotated by 90° counterclockwise about the origin,

Rule to be followed,

A(x, y) → P(-y, x)

Therefore, A(1, 1) → P(-1, 1)

Similarly, B(3, 2) → Q(-2, 3)

C(2, 5) → R(-5, 2)

Triangle given in second quadrant will be the triangle PQR.

If the point P of triangle PQR is reflected across a line y = x,

Rule to be followed,

P(x, y) → X(y, x)

P(-1, 1) → X(1, -1)

Similarly, Q(-2, 3) → Y(3, -2)

R(-5, 2) → Z(2, -5)

Therefore, triangle given in fourth quadrant is triangle XYZ.

6 0
3 years ago
Find all polar coordinates of point p where p = (6, -pi/5)
Lelu [443]
Given a point in coordinates form (r,\theta), one can compute the cartesian form like this:
(r\cos\theta,r\sin\theta )
We have:
r=6,\theta=-\dfrac{\pi}{5}
We get the cartesian form then:
\left(6\cos-\dfrac{\pi}{5},6\sin-\dfrac{\pi}{5}\right)
4 0
3 years ago
Pleaseeeeeee help mee
BlackZzzverrR [31]

Answer:

The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

Step-by-step explanation:

<u><em>Step(i):</em></u>-

Given  

                cos( 3x - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

                  cos( 3x - \frac{\pi }{3} )  = cos (\frac{\pi }{6} )

                      3x - \frac{\pi }{3}  =  \frac{\pi }{6}

                      3x - \frac{\pi }{3  } + \frac{\pi }{3}   =  \frac{\pi }{6} + \frac{\pi }{3}

                      3x = \frac{2\pi +\pi }{6} = \frac{3\pi }{6} = \frac{\pi }{2}

                     x = \frac{\pi }{6}

<u><em>Step(ii)</em></u>:-

The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

<u><em>verification </em></u>:-

      cos( 3x - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

put  x = \frac{\pi }{6}

    cos( 3(\frac{\pi }{6})  - \frac{\pi }{3} )  = \frac{\sqrt{3} }{2}

    cos (\frac{\pi }{6} ) = \frac{\sqrt{3} }{2} \\\\\frac{\sqrt{3} }{2} =  \frac{\sqrt{3} }{2}

Both are equal

∴The solution of the given trigonometric equation

                   x = \frac{\pi }{6}

                     

4 0
2 years ago
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Luba_88 [7]

QUESTION:

When you factor a little perfect square trinomial, which pattern results?

ANSWER:

[2] The square of a binomial pattern.

EXPLANATION:

<u>Squaring a binomial creates a perfect square trinomial</u>:–

  • (a + b)²
  • (a - b)²
8 0
2 years ago
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