Tan2x=___

Mathematics

1 answer:

SSSSS [86.1K]2 years ago

7 0

Step-by-step explanation:

tan2x = sin2x/cos2x

we know that ,

sin2x = 2sinxcosx
sin2x = 2sinxcosx cos2x = cos²x - sin²x

Since, tan2x = 2sinx*cosx/cos²x- sin²x

Dividing by cos²x in numerator and denominator.

We get ,

tan2x = 2sinx/cosx / 1- sin²x/cos²x

Since, we get tan2x= 2tanx/1-tan²x

Option (c) is correct option.

Hope it will be helpful

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The coordinates of AB are A(-5, -1) and B(-2, -6). If AC : CB = 3 : 7, what are the coordinates of point C?

bixtya [17]

$\text{Let the coordinates of AB are }A(-5,-1), \text{ and }B(-2, -6)\\
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\text{let the coordinate of th point C be (x, y), such that}\\
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AC:CB=3:7\\
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\text{By the section formula, we know that if P(x,y) lies on a line segment AB}\\
\text{where, }A(x_1,y_1), \ B(x_2,y_2)\text{ and satisfy the ratio, }AP:PB=m:n, \text{ then}$

$P=\left ( \frac{mx_2+nx_1}{m+n}, \ \frac{my_2+ny_1}{m+n} \right ).\\
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\text{So using this formula, we get for the given problem}\\
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C=\left ( \frac{3(-2)+7(-5)}{3+7}, \ \frac{3(-6)+7(-1)}{3+7} \right )\\
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\Rightarrow C=\left ( \frac{-6-35}{10}, \ \frac{-18-7}{10} \right )\\
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\Rightarrow C=\left ( \frac{-41}{10}, \ \frac{-25}{10} \right )\\
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\Rightarrow C=\left ( -4.1, \ -2.5 \right )$