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ipn [44]
3 years ago
11

Verify the identity: cot^3t/csct = cost(csc^2t-1)

Mathematics
1 answer:
cestrela7 [59]3 years ago
7 0
We know that cot = cos/sin
then cot^3 = cos^3 / sin ^3
we also know that csc = 1/sin
then 1/csc = sin
cot^3t/csct =(cos^3t / sin^3t) * sint =cos^3t / sin^2t
1+cot^2 = csc^2
csc^2 -1 = cot^2
cost(csc^2t-1) =cost(cot^2t)
cost( cos^2t/sin^2t) =cos^3t/sin^2t
It implies that both sides are equal

hope it helps
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melisa1 [442]

The equation of the line in the point-slope form is y - 15 = -\frac{3}{2} (x - 10)

Step-by-step explanation:

The point-slope form of a linear equation is y-y_{1}=m(x-x_{1}) , where

  • m is the slope of the line, where m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} , (x_{1},y_{1}) and (x_{2},y_{2}) are two points on the line
  • (x_{1},y_{1}) is a point on the line

∵ Point A = (10 , 15)

∵ The x-coordinate of the second point is 125% of x-coordinate

  of point A

∴ x-coordinate of second point = \frac{125}{100} × 10

∴ x-coordinate of second point = 12.5

∵ The y-coordinate of the second point is 75% of y-coordinate

  of point A

∴ y-coordinate of second point = \frac{75}{100} × 15

∴ y-coordinate of second point = 11.25

∴ The coordinates of the second point are (12.5 , 11.25)

Let us find the slope of the line by using the rule of it above

∵ (x_{1},y_{1}) = (10 , 15)

∵ (x_{2},y_{2}) = (12.5 , 11.25)

∴ m=\frac{11.25-15}{12.5-10}=\frac{-3.75}{2.5}=-\frac{3}{2}

Now we can write the equation

∵ The point-slope form is y-y_{1}=m(x-x_{1})

∵ m=-\frac{3}{2}

∵ (x_{1},y_{1}) = (10 , 15)

- Substitute these values in the form of the equation

∴ y - 15 = -\frac{3}{2} (x - 10)

The equation of the line in the point-slope form is y - 15 = -\frac{3}{2} (x - 10)

Learn more:

You can learn more about the linear equation in brainly.com/question/4152194

#LearnwithBrainly

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