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avanturin [10]
3 years ago
10

Can someone write out the steps on how to verify this identity?

Mathematics
1 answer:
zhenek [66]3 years ago
3 0

Step-by-step explanation:

(csc θ − 1) / cot θ

Multiply top and bottom by the conjugate csc θ + 1.

(csc θ − 1) (csc θ + 1) / (cot θ (csc θ + 1))

Distribute.

(csc²θ − 1) / (cot θ (csc θ + 1))

Use Pythagorean identity.

cot²θ / (cot θ (csc θ + 1))

Divide.

cot θ /  (csc θ + 1)

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Answer quick for brainliest
umka2103 [35]

Answer:

y=-1x-5

Step-by-step explanation:

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3 years ago
5) In the figure, triangle ABC is a right triangle at B. If CD = 15, find BC to the nearest tenth.
ycow [4]

Answer:

BC ≈ 4.0

Step-by-step explanation:

∠ DCA = 180° - 70° = 110° ( adjacent angles )

∠ DAC = 180° - (30 + 110)° ← sum of angles in triangle

∠ DAC = 180° - 140° = 40°

Using the Sine rule in Δ ACD to find common side AC

\frac{AC}{sin30} = \frac{15}{sin40} ( cross- multiply )

AC × sin40° = 15 × sin30° ( divide both sides by sin40° )

AC = \frac{15sin30}{sin40} ≈ 11.668

Using the cosine ratio in right triangle ABC

cos70° = \frac{adjacent}{hypotenuse} = \frac{BC}{AC} = \frac{BC}{11.668} ( multiply both sides by 11.668 )

11.668 × cos70° = BC , then

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6 0
3 years ago
Find the volume of the cone
maksim [4K]
The volume is 800pi cubic feet

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Which equation is equivalent to<br> Sq rt x+ 11 = 15?
vladimir2022 [97]
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How to find height of a triangular prism where length is 9, width is 3.5, and height is unknown. Volume is 50.4, and explain ans
riadik2000 [5.3K]
*The width in your question - I assumed it is refers to the height of the triangle base.

Volume of a triangle prism = base area x height

The base is a triangle:
Volume of a triangle prism = (1/2 x base x height₁) x height₂

Plug in the values and solve for height₂:

50.4 = (1/2 x 9 x 3.5) x height

50.4 = 15.75 x height

height = 50.4 ÷ 15.75

height = 3.2 units

-----------------------------------------
Answer: Height = 3.2 units
-----------------------------------------
5 0
3 years ago
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