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Luda [366]
3 years ago
11

If tan theta =3, find the value of tan theta + tan (theta+pi) + tan (theta +2pi)

Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
4 0

Answer:

tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9

Step-by-step explanation:

Given

tan\theta = 3

Required

Find

tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)

Calculate tan(\theta + \pi) \ and\ tan(\theta+2\pi)

Using tan rule

tan(\theta + \pi)  = \frac{tan\theta + tan\pi}{1 - tan\theta tan\pi}

So:

tan(\theta + \pi)  = \frac{tan\theta + 0}{1 - tan\theta *0}

tan(\theta + \pi)  = \frac{tan\theta}{1 }

tan(\theta + \pi)  = \tan\theta

tan(\theta+2\pi)

tan(\theta + 2\pi)  = \frac{tan\theta + tan2\pi}{1 - tan\theta tan2\pi}

tan(\theta + 2\pi)  = \frac{tan\theta + 0}{1 - tan\theta *0}

tan(\theta + 2\pi)  = \tan\theta'

'So:

tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = tan\theta +tan\theta +tan\theta

tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 3+3+3

tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9

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Hello,

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I_1=1\\






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3 years ago
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3 years ago
Sarah has a collection of nickels, dimes, and quarters worth $28.75. She has 10 more dimes than nickels and twice as many quarte
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Answer:

Step-by-step explanation:

Write an equation for each statement:

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"She has 10 more dimes than nickels"

d = n + 10

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"twice as many quarters as dimes."

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How many coins of each kind does she have?

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Take the 2nd equation and arrange it so n is in terms of d also

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The statement "She has 10 more dimes than nickels"

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Check our solutions

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2 years ago
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2 .............:)
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