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Drupady [299]
3 years ago
13

Plzzzz help and I'll give you brainliest ​

Mathematics
1 answer:
sdas [7]3 years ago
3 0

Step-by-step explanation:

Left hand side:

4 [sin⁶ θ + cos⁶ θ]

Rearrange:

4 [(sin² θ)³ + (cos² θ)³]

Factor the sum of cubes:

4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]

Pythagorean identity:

4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]

Complete the square:

4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]

4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]

Pythagorean identity:

4 [1 − 3 sin² θ cos² θ]

Rearrange:

4 − 12 sin² θ cos² θ

4 − 3 (2 sin θ cos θ)²

Double angle formula:

4 − 3 (sin (2θ))²

4 − 3 sin² (2θ)

Finally, apply Pythagorean identity and simplify:

4 − 3 (1 − cos² (2θ))

4 − 3 + 3 cos² (2θ)

1 + 3 cos² (2θ)

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Under a certain transformation T, AA'BC' is the image of AABC. The perimeter of AA'B'C' is twice the perimeter of ABC. What kind
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which indicates that the transformation is a dilation.

  • The transformation <em>T</em> is; <u>a dilation transformation with a scale factor of 2, D₂</u>

Reasons:

The transformation applied to ΔABC = T

The image of ΔABC following the transformation, T = ΔA'B'C'

The perimeter of ΔA'B'C' = Twice the perimeter of ΔABC

Therefore, we have;

A'B' + B'C' + A'C' = 2 × (AB + BC + AC)

Which gives

A'B' + B'C' + A'C' = 2·AB + 2·BC + 2·AC

By similar triangles, we have the ratio of corresponding sides as follows;

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Which gives;

\displaystyle \frac{AB}{A'B'}  = \frac{AB}{2 \cdot AB} = \frac{1}{2}

A'B' = 2·AB

Therefore;

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Learn more about dilation transformation here:

brainly.com/question/2458912

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