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2 years ago

Tan^2 A - sin^2 A = tan^2 A.sin^2 A

Mathematics

1 answer:

ella [17]2 years ago

3 0

Answer:

step by step calculation :

To proof:

tan²A - sin²A = tan² A sin²A

from LHS,

tan²A -sin²A

= (sin²A / cos²A) - sin²A……[tan A=sin A/cos A]

= (sin²A - sin²Acos²A) / cos²A

= sin²A (1- cos²A) / cos² A [tan A = sinA / cos A]

= tan²A sin²A= RHS

.•. hence proved

hope it helped:)

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The equation of line is: $\mathbf{4x-3y=-18}$

Step-by-step explanation:

We need to find an equation of the line that passes through the points (-6, -2) and (-3, 2)?

The equation of line in slope-intercept form is: $y=mx+b$

where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding Slope

Slope can be found using formula: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have $x_1=-6,y_1=-2, x_2=-3, y_2=2$

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$Slope=\frac{2-(-2)}{-3-(-6)}\\Slope=\frac{2+2}{-3+6} \\Slope=\frac{4}{3}$

So, we get slope: $m=\frac{4}{3}$

Finding y-intercept

Using point (-6,-2) and slope $m=\frac{4}{3}$ we can find y-intercept

$y=mx+b\\-2=\frac{4}{3}(-6)+b\\-2=4(-2)+b\\-2=-8+b\\b=-2+8\\b=6$

So, we get y-intercept b= 6

Equation of required line

The equation of required line having slope $m=\frac{4}{3}$ and y-intercept b = 6 is

$y=mx+b\\y=\frac{4}{3}x+6$

Now transforming in fully reduced form:

$y=\frac{4x+6*3}{3} \\y=\frac{4x+18}{3} \\3y=4x+18\\4x-3y=-18$

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2 years ago

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3 years ago

What is the following simplified product? Assume x greater-than-or-equal-to 0 2 StartRoot 8 x cubed EndRoot (3 StartRoot 10 x Su

dalvyx [7]

The simplified expression of 2√8x³(3√10x⁴ - x√5x²) is 24x³√5x - 4x³√10x

<h3>How to determine the simplified product?</h3>

The complete question is added as an attachment

From the attached figure, the product expression is:

2√8x³(3√10x⁴ - x√5x²)

Evaluate the exponents

2√8x³(3√10x⁴ - x√5x²) = 2 *2x√2x(3x²√10 - x²√5)

Evaluate the products

2√8x³(3√10x⁴ - x√5x²) = 4x√2x(3x²√10 - x²√5)

Open the bracket

2√8x³(3√10x⁴ - x√5x²) = 12x³√20x - 4x³√10x

Evaluate the exponents

2√8x³(3√10x⁴ - x√5x²) = 24x³√5x - 4x³√10x

Hence, the simplified expression of 2√8x³(3√10x⁴ - x√5x²) is 24x³√5x - 4x³√10x

Tan^2 A - sin^2 A = tan^2 A.sin^2 A​

Tan^2 A - sin^2 A = tan^2 A.sin^2 A