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IrinaK [193]
3 years ago
15

Using addition formula solve tan 15​

Mathematics
1 answer:
salantis [7]3 years ago
3 0

Answer:

2 - \sqrt{3}

Step-by-step explanation:

Using the addition formula for tangent

tan(A - B) = \frac{tanA-tanB}{1+tanAtanB} and the exact values

tan45° = 1 , tan60° = \sqrt{3} , then

tan15° = tan(60 - 45)°

tan(60 - 45)°

= \frac{tan60-tan45}{1+tan60tan45}

= \frac{\sqrt{3}-1 }{1+\sqrt{3} }

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.

The conjugate of 1 + \sqrt{3} is 1 - \sqrt{3}

= \frac{(\sqrt{3}-1)(1-\sqrt{3})  }{(1+\sqrt{3})(1-\sqrt{3})  } ← expand numerator/denominator using FOIL

= \frac{\sqrt{3}-3-1+\sqrt{3}  }{1-3}

= \frac{-4+2\sqrt{3} }{-2}

= \frac{-4}{-2} + \frac{2\sqrt{3} }{-2}

= 2 - \sqrt{3}

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Answer:

63mm

Step-by-step explanation:

7mm+8mm=15.

15×15=225

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4 0
3 years ago
5(-2 -2p) simplify expression
I am Lyosha [343]

Answer:

-10 -10p

Step-by-step explanation:

5(-2 -2p)

Distribute the 5

5*-2 +5(-2p)

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6 0
3 years ago
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Please HELP I WILL REWARD BRAINLIEST ANSWER IM VERY CONFUSED
ozzi
Dilation is either : enlargement or shirking.

Simply you multiply the ordered pair times the dilation vector (Origin-Centered) 

D.F = dilation factor;


d.f  = 5

C' = d.fC

when you multiply a constant times an ordered pair , it multiples into each of the pair.


C' = 5 ( -5 , 1 ) = ( -25, 5 ) 

In case you were asked for A' , B' (test yourself before checking) 



A' = 5 (-4,3) = ( -20 , 15)

B' = 5 ( 2, 3 ) = ( 10, 15) 

Dividing the dilated by the original pair results in the dilation factor

A'/A =  (-20/15)/(-4,3) = 5(-4,3)/(-4,3) = 5 
4 0
3 years ago
It costs $120 for 20 students to visit an aquarium. How much does it cost for 152 students? Set up a proportion to solve.​
nordsb [41]

Answer:

152 times 6=912

Step-by-step explanation:

$120 for every 20 students

it cost $6 for every 1 student

$6 times 152=912

5 0
3 years ago
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USPshnik [31]
25 feet above sea level means she travelled 25 feet to the surface of the sea. She would have to descend (37-25=12) 12 more feet to achieve 37 total feet of travel, so she descended 12 feet below sea level.
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3 years ago
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