Traditional method: used by humans when they learnt counting and when fraction came into existence.Suppose something(Area of a field) is divided into parts and another thing(Amount of water used in irrigating the field) is divided into parts and then we have to multiply these two numbers.

3 0

3 years ago

Root 3 cosec140° - sec140°=4 prove that

Lorico [155]

Answer:

Step-by-step explanation:

We are to show that $\sqrt{3} cosec140^{0} - sec140^{0} = 4\\$

Proof:

From trigonometry identity;

$cosec \theta = \frac{1}{sin\theta} \\sec\theta = \frac{1}{cos\theta}$

$\sqrt{3} cosec140^{0} - sec140^{0} \\= \frac{\sqrt{3} }{sin140} - \frac{1}{cos140} \\= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\$

From trigonometry, 2sinAcosA = Sin2A

$= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\\\= \frac{\sqrt{3}cos140-sin140 }{sin280/2}\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{2sin280}\\\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{sin280}\\since sin420 = \sqrt{3}/2 \ and \ cos420 = 1/2 \\ then\\\frac{4(sin420cos140-cos420sin140) }{sin280}$

Also note that sin(B-C) = sinBcosC - cosBsinC

sin420cos140 - cos420sin140 = sin(420-140)

The resulting equation becomes;

$\frac{4(sin(420-140)) }{sin280}$

= $\frac{4sin280}{sin280}\\ = 4 \ Proved!$

3 0

3 years ago

What is the equation, in point-slope form, for a line that goes through (8, −4)) and has a slope of −56 ?

grin007 [14]

Y - y1 = m(x - x1)
slope(m) = -56
(8,-4)...x1 = 8 and y1 = -4
now we sub...pay close attention to ur signs
y - (-4) = -56(x - 8)....not finished yet
y + 4 = -56(x - 8) <===

6 0

3 years ago

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