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andreev551 [17]
2 years ago
9

Which expression best completes the following definition of a complex number?

Mathematics
2 answers:
k0ka [10]2 years ago
7 0

Answer:

C. a+bi

I took the test

Degger [83]2 years ago
5 0
The answer is Isd= uyju love
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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
ABCD is a trapezoid. Point E is the midpoint of AD and point F is the midpoint of B.
VikaD [51]
2 cm. because you would subtract 5 and 3.
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3 years ago
Matt and Cat win £120 on the lottery and decide to share the winning ratio 1:2
8_murik_8 [283]
The way to work out how much each person gets is to find out how much one part is worth.

We can do this by adding the ratio (1:2) which gives us 3.

Divide £120 by 3 parts and you get £40 as one part. 

Because the ratio is one part : two parts, Matt gets £40 and Cat gets £80. 
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3 years ago
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You are asked to draw a triangle with side lengths of 6 inches and 8 inches. What is the longest whole number length that your t
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Fo sides, a,b,c
where c is the longest

c<a+b
or else you won't have a triangle

we want the longest side
this mystery side is c
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c<6+8
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the next largest whole number is 13

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What is 604,838 rounded to the nearest whole number ?
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Answer:

604,838 already is a whole number.

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3 years ago
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