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3 years ago

Are they congruent? Yes Congruence method: Congruence statement:

Mathematics

1 answer:

miskamm [114]3 years ago

3 0

Yessssssssssssssssss

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(x sin a + y cos a)^2 + (x cos a – y sin a)^2 = x^2 + y^2

kobusy [5.1K]

Answer:

Proved

Step-by-step explanation:

Required

Prove that:

$(x\ sin\ a + y\ cos\ a)^2 + (x\ cos\ a - y\ sin\ a)^2 = x^2 + y^2$

Solving from left to right:

Open brackets

$(x\ sin\ a + y\ cos\ a)(x\ sin\ a + y\ cos\ a) + (x\ cos\ a - y\ sin\ a)(x\ cos\ a - y\ sin\ a) = x^2 + y^2$ $x^2\ sin^2 a + 2xy\ sin\ a\ cos\ a + y^2\ cos^2 a + x^2\ cos^2 a - 2xy\ sin\ a\ cos\ a + y^2\ sin^2 a = x^2 + y^2$

Collect Like Terms

$x^2\ sin^2 a + 2xy\ sin\ a\ cos\ a - 2xy\ sin\ a\ cos\ a + y^2\ cos^2 a + x^2\ cos^2 a+ y^2\ sin^2 a = x^2 + y^2$

$x^2\ sin^2 a + y^2\ cos^2 a + x^2\ cos^2 a+ y^2\ sin^2 a = x^2 + y^2$

Collect Like Terms

$x^2\ sin^2 a + y^2\ sin^2 a + x^2\ cos^2 a + y^2\ cos^2 a = x^2 + y^2$

Factorize:

$(x^2 + y^2)\ sin^2 a + (x^2 + y^2) cos^2 a = x^2 + y^2$

Further factorize

$(x^2 + y^2)(sin^2 a + cos^2 a) = x^2 + y^2$

In trigonometry:

$sin^2 a + cos^2 a = 1$

So, we have:

$(x^2 + y^2)(1) = x^2 + y^2$

$x^2 + y^2 = x^2 + y^2$

<em>Proved</em>

6 0

3 years ago

olga nikolaevna [1]

D=t + 7.5 hope this helps

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3 years ago

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Let f(x)= -5x+6. Find and simplify f(3b-5).

slamgirl [31]

Answer:

-15b+31

Step-by-step explanation:

f(x)=-5x+6

f(3b-5)=-5(3b-5)+6=-15b+25+6=-15b+31

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3 years ago

The figure below shows a square ABCD and an equilateral triangle DPC:

Allisa [31]

Answer:

Which of the following completes Ted's proof?

In square ABCD; angle ADC = angle BCD

In square ABCD; angle ADP = angle BCP

In triangles APD and BPC; angle ADC = angle BCD

In triangles APD and BPC; angle ADP = angle BCP\

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2 years ago

M=3 (5,15) pleaseeeeeeeeeee help .

jeka57 [31]

Answer:

m=15.45?

Step-by-step explanation:

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3 years ago

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