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PSYCHO15rus [73]
3 years ago
14

Can someone please help

Mathematics
1 answer:
Fynjy0 [20]3 years ago
8 0

Answer:

angle C = 78

angle D = 108

Step-by-step explanation:

the measure of angle A is 102

To find the measure of angle C

let Angle C be x

102 + x = 180 (linear pair)

x = 180 -102

x = 78

angle C = 78

angle B = 78 (vertically opposite angles are equal)

angle D = 108 (vertically opposite angles are equal)

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Subtract (2x+1) from (4x^2 +4x + 8)
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Show that xcosec^2x = cotx - d/dx xcotx
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In the question, we are asked to show that x.cosec²x = cot x - d/dx x.cot x.

To prove, we go by the right-hand side of the equation:

cot x - d/dx x.cot x.

We solve the differential d/dx using the product rule, according to which, d/dx uv = u. d/dx(v) + v. d/dx(u), where u and v are functions of x.

cot x - {x. d/dx(cot x) + cot x. d/dx(x)}

= cot x - {x. (-cosec²x) + cot x} {Since, d/dx(cot x) = -cosec²x, and d/dx(x) = 1}

= cot x + x. cosec²x - cot x

= x. cosec²x

= The left-hand side of the equation.

Thus, the given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

Learn more about differentials at

brainly.com/question/14830750

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