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Misha Larkins [42]
3 years ago
14

1+sinx+cosx/1+sinx-cosx=1+cosx/sinx help pls by proving

Mathematics
1 answer:
Monica [59]3 years ago
6 0

Answer:

Below.

Step-by-step explanation:

I'll  write sin x as s and cos x as c so we have:

(1 + s +c)/(1 + s - c) = (1 + c)/s

Cross multiplying:

s + s^2 + cs  = 1 + s - c + c + cs - c^2

s  + s^2 + cs = 1 + s + cs - c^2

s^2 + c^2 + s - s + cs - cs = 1

s^2 + c^2 = 1.

- that is sin^2 x + cos^2 x = 1 which is a known identity.

Therefore the original identity is proved.

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MrRissso [65]

Answer:

1. \dfrac{4}{3}

2. y=6x-11

3. 4

Step-by-step explanation:

The equation of the line that passes trough the points A(14,-1) and B(2,1) is

\dfrac{x-14}{2-14}=\dfrac{y-(-1)}{1-(-1)},\\ \\\dfrac{x-14}{-12}=\dfrac{y+1}{2},\\ \\y+1=-\dfrac{1}{6}(x-14),\\ \\y=-\dfrac{1}{6}x+\dfrac{7}{3}-1,\\ \\y=-\dfrac{1}{6}x+\dfrac{4}{3}.

The y-intercept of this line is

y=-\dfrac{1}{6}\cdot 0+\dfrac{4}{3}=\dfrac{4}{3}.

Line BC is perpendicular to line AB, then its slope is 6. Line BC passes through the point B, so

y-1=6(x-2),\\ \\y-1=6x-12,\\ \\y=6x-11.

If the y-coordinate of point C is 13, then x-coordinate is

13=6x-11,\\ \\6x=13+11,\\ \\6x=24,\\ \\x=4.

7 0
3 years ago
Help needed!!! Will give 20 points!!!
beks73 [17]

Answer:

1st answer

Step-by-step explanation:

f(g(x)) = f(4x)=(4x)^2-8(4x)+4\\=16x^2-32x+4

7 0
3 years ago
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Mazyrski [523]

Answer:

37.79924

Step-by-step explanation:

5 0
3 years ago
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A line has a slope of 5/6 and a y-intercept of -3.
SVEN [57.7K]
The answer would be the first option :)
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3 years ago
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Can someone explain to me how this has multiple answers? I really don't understand! When I did it I only got the first answer. P
Vesna [10]

in \: firt \: quadrant \\ sin \frac{\pi}{4}  =  \frac{ \sqrt{2} }{2}  \\ in \: second \: quadrant \\ sin \frac{3\pi}{4} =  \frac{ \sqrt{2} }{2}  \\ in \: third \: quadrant \:  \\ sin \frac{5\pi}{4}  = \frac{ -  \sqrt{2} }{2}  \\ in \: forth \: quadrant \\  sin \frac{7\pi}{4}  =  - \frac { \sqrt{ 2} }{2}  \\ in \: this \: way \: it \: has \: multiple \: soution

3 0
3 years ago
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