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3 years ago

7

Verify the Identity. tan²xsin²x = tan²x-sin²x

1 answer:

Aleonysh [2.5K]3 years ago

4 0

tan²(<em>x</em>) - sin²(<em>x</em>) = sin²(<em>x</em>)/cos²(<em>x</em>) - sin²(<em>x</em>)

… = sin²(<em>x</em>) (1/cos²(<em>x</em>) - 1)

… = sin²(<em>x</em>) (sec²(<em>x</em>) - 1)

… = sin²(<em>x</em>) tan²(<em>x</em>)

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Solve the system of equation by guess sidle method

lilavasa [31]

Answer: The solution is,

$x_1\approx 0.876$

$x_2\approx 0.419$

$x_3\approx 0.574$

Step-by-step explanation:

Given equations are,

$8x_1 + x_2 + x_3 = 8$

$2x_1 + 4x_2 + x_3 = 4$

$x_1 + 3x_2 + 5x_3 = 5$ ,

From the above equations,

$x_1=\frac{1}{8}(8-x_2-x_3)$

$x_2=\frac{1}{4}(4-2x_1-x_3)$

$x_3=\frac{1}{5}(5-x_1-3x_2)$

First approximation,

$x_1(1)=\frac{1}{8}(8-(0)-(0))=1$

$x_2(1)=\frac{1}{4}(4-2(1)-(0))=0.5$

$x_3(1)=\frac{1}{5}(5-1-3(0.5))=0.5$

Second approximation,

$x_1(2)=\frac{1}{8}(8-(0.5)-(0.5))=0.875$

$x_2(2)=\frac{1}{4}(4-2(0.875)-(0.5))=0.4375$

$x_3(2)=\frac{1}{5}((0.875)-3(0.4375))=0.5625$

Third approximation,

$x_1(3)=\frac{1}{8}(8-(0.4375)-(0.5625))=0.875$

$x_2(3)=\frac{1}{4}(4-2(0.875)-(0.5625))=0.421875$

$x_3(3)=\frac{1}{5}(5-(0.875)-3(0.421875))=0.571875$

Fourth approximation,

$x_1(4)=\frac{1}{8}(8-(0.421875)-(0.571875))=0.875781$

$x_2(4)=\frac{1}{4}(4-2(0.875781)-(0.571875))=0.419141$

$x_3(4)=\frac{1}{5}(5-(0.875781)-3(0.419141))=0.573359$

Fifth approximation,

$x_1(5)=\frac{1}{8}(8-(0.419141)-(0.573359))=0.875938$

$x_2(5)=\frac{1}{4}(4-2(0.875938)-(0.573359))=0.418691$

$x_3(5)=\frac{1}{5}(5-(0.875938)-3(0.418691))=0.573598$

Hence, by the Gauss Seidel method the solution of the given system is,

$x_1\approx 0.876$

$x_2\approx 0.419$

$x_3\approx 0.574$

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3 years ago

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Step-by-step explanation:

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What is the value of 2+3n if n= 1/2

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4 years ago

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The perimeter of a rectangle is 38 inches. If the length of the rectangle is 14 inches, which equation could be used to find the

Solnce55 [7]

Perimeter, P = 2*(L + W)

Length, L = 14, Width = x

P = 2*(L + W)

38 = 2*(14 + x).

2*(14 + x) = 38, is the equation used to find x.

Let's go ahead and solve for x, though the question did not ask us to solve it.

14 + x = 38/2

14 + x = 19

x = 19 - 14

x = 5

Width is 5 inches.

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3 years ago