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Nikolay [14]
3 years ago
6

Name a pair of perpendicular lines

Mathematics
1 answer:
lesantik [10]3 years ago
8 0

Answer:

90 degree angled lines

Step-by-step explanation:


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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!!

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2 years ago
Marshall has an account balance of<br> -$49.18. Does Marshall owe the bank more or less than $50?
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Answer:

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gtnhenbr [62]

Answer:

50.25 cm trust me

Step-by-step explanation:

5.25 cm

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Simplify V45 (square root 45) fully, giving your answer in the form aVb (square root)
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Answer:

B

Step-by-step explanation:

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2 years ago
von has a rectangular workroom with a perimeter of 26 feet the length of the workrooms is 6 feet what is the width of vons workr
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The answer is 7 because 2 times 6 equals 12 + 26 - 12 equals 14 + 14 divided by 2 equals 7 this is how I see you it out the answer again the answer is seven feet feet
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