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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:

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Step-by-step explanation:

The equation of the line in Slope-intercept form  is:

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You can identify that:

m=1

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m=1

b. The equation of the line in Point-slope form is:

y -y_1 = m(x - x_1)

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Given the point (-4,2), substitute this point and the slope of the line into the equation:

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Give a value to "x", substitute it into this equation and solve for "y":

For x=1 :

y -2 = (1 +4)

y= 5+2

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c. The slopes of perpendicular lines are negative reciprocals, then the  slope of a line perpendicular to the given line is:

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d. Given the point (-4,2), substitute this point and the slope of the line into the equation:

 y -2 = -1(x +4)

 y -2 = -(x +4)

Give a value to "x", substitute it into this equation and solve for "y":

For x=3 :

y -2 = -(3 +4)

y= -7+2

y= -5

Then, you get the point (3,-5)

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