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Gnesinka [82]
2 years ago
7

I just need to know what the answer is pls help!! ty!!

Mathematics
1 answer:
zhannawk [14.2K]2 years ago
4 0

Answer:

Tangent is the answer.

Hope it helps!!!

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Prove that: [1 + 1/tan²theta] [1 + 1/cot² thata] = 1/(sin²theta - sin⁴theta]
Stels [109]

Step-by-step explanation:

<h3><u>Given :-</u></h3>

[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]

<h3><u>Required To Prove :-</u></h3>

[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)

<h3><u>Proof :-</u></h3>

On taking LHS

[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]

We know that

Tan θ = 1/ Cot θ

and

Cot θ = 1/Tan θ

=> (1+Cot²θ)(1+Tan²θ)

=> (Cosec² θ) (Sec²θ)

Since Cosec²θ - Cot²θ = 1 and

Sec²θ - Tan²θ = 1

=> (1/Sin² θ)(1/Cos² θ)

Since , Cosec θ = 1/Sinθ

and Sec θ = 1/Cosθ

=> 1/(Sin²θ Cos²θ)

We know that Sin²θ+Cos²θ = 1

=> 1/[(Sin²θ)(1-Sin²θ)]

=> 1/(Sin²θ-Sin²θ Sin²θ)

=> 1/(Sin²θ - Sin⁴θ)

=> RHS

=> LHS = RHS

<u>Hence, Proved.</u>

<h3><u>Answer:-</u></h3>

[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)

<h3><u>Used formulae:-</u></h3>

→ Tan θ = 1/ Cot θ

→ Cot θ = 1/Tan θ

→ Cosec θ = 1/Sinθ

→ Sec θ = 1/Cosθ

<h3><u>Used Identities :-</u></h3>

→ Cosec²θ - Cot²θ = 1

→ Sec²θ - Tan²θ = 1

→ Sin²θ+Cos²θ = 1

Hope this helps!!

7 0
2 years ago
A record album is 3/16 of an inch thick. How many albums can be stacked to fit in a box 12 inches high? Please show me how you g
german
Hope this was helpful

5 0
3 years ago
What is the scale factor of ABC to DEF?
pochemuha

Answer:

A. 1

Step-by-step explanation:

<em>Scale Factor:</em>

<em>The scale factor is the number you multiply the length of a side of the first triangle to get the length of the corresponding side of the other triangle.</em>

Every side that measures 5 in triangle ABC has a corresponding side in triangle DEF that also measures 5. In this case 5 * 1 = 5, so the scale factor is 1.

Answer: A. 1

5 0
3 years ago
Read 2 more answers
N divided by 2 - 6 = 8
dybincka [34]

Answer:

N=28 my friend

Step-by-step explanation:

7 0
3 years ago
Part A.) A garden hose supplies 36 gallons of water in 3 minutes. Use a table of equivalent ratios to show the garden house's wa
saw5 [17]

Answer: It would be 360 gallons of water per 10 mins because

Step-by-step explanation:

You multiply 36×10 and you get 360 gallons

7 0
3 years ago
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