3 years ago

The expression 6(x − 5)

Mathematics

1 answer:

grigory [225]3 years ago

5 0

Answer:

6x-30

Step-by-step explanation:

expand the brackets

6×x

6×-5

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Using addition formula solve tan 15

salantis [7]

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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