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How do you prove that 2 sin 3x divided by sin x plus 2 cos 3x divided by cos x equals 8 cos 2x?
You need to know the trigonometric formulae for sin and cos of compound angles.
sin(x+y) = sin(x)*cos(y)+cos(x)*sin(y)
and
cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y)
Using these, y = x implies that
sin(2x) = sin(x+x) = 2*sin(x)cos(x)
and
cos(2x) = cos(x+x) = cos^2(x) - sin^2(x)
Next, the triple angle formulae are:
sin(3x) = sin(2x + x) = 3*sin(x) - 4*sin^3(x)
and
cos(3x) = 4*cos^3(x) - 3*cos(x)
Then the left hand side
= 2*[3*sin(x) - 4*sin^3(x)]/sin(x) + 2*[4*cos^3(x) - 3*cos(x)]/cos(x)
= 6 - 8*sin^2(x) + 8cos^2(x) - 6
= 8*[cos^2(x) - sin^2(x)]
= 8*cos(2x) = right hand side.
What else can I help you with?
Prove that sin 90 equals cos 50sin 40- cos 40 sin 50?
Sorry, but cos(50)sin(40) - cos(40)sin(50) is -0.1736, which is not even close to sin(90) which is 1.This does not work in radians, either. Please restate your question.
If the csc equals 2 divided by 7 what is cos?
How is it possible that the value of cosecant is less than 1 (2/7)?
If a cos theta plus b sin theta equals 8 and a sin theta - b cos theta equals 5 show that a squared plus b squared equals 89?
Well, darling, if we square the first equation and the second equation, add them together, and do some algebraic magic, we can indeed show that a squared plus b squared equals 89. It's like a little math puzzle, but trust me, the answer is as sassy as I am.
Cot 70 plus 4cos70 equals?
cot 70 + 4 cos 70 = cos 70 / sin 70 + 4 cos 70 = cos 70 (1/sin 70 + 4) = cos 70 (csc 70 + 4) Numerical answer varies, depending on whether 70 is in degrees, radians, or grads.
How does sin2x divided by 1-cosx equal 1 plus cosx?
sin2x / (1-cos x) = (1-cos2x) / (1-cos x) = (1-cos x)(1+cos x) / (1-cos x) = (1+cos x) sin2x=1-cos2x as sin2x+cos2x=1 1-cos2x = (1-cos x)(1+cos x) as a2-b2=(a-b)(a+b)
Verify that sin minus cos plus 1 divided by sin plus cos subtract 1 equals sin plus 1 divided by cos?
[sin - cos + 1]/[sin + cos - 1] = [sin + 1]/cosiff [sin - cos + 1]*cos = [sin + 1]*[sin + cos - 1]iff sin*cos - cos^2 + cos = sin^2 + sin*cos - sin + sin + cos - 1iff -cos^2 = sin^2 - 11 = sin^2 + cos^2, which is true,
What equals 1 cos squared x divided by cos squared x?
1. Anything divided by itself always equals 1.
How do you prove cot squared theta plus cos squared theta plus sin squared theta scs squared theta?
Until an "equals" sign shows up somewhere in the expression, there's nothing to prove.
Cos x equals -cos x plus 1?
No, but cos(-x) = cos(x), because the cosine function is an even function.
Sin 15 plus cos 105 equals?
Sin 15 + cos 105 = -1.9045
What is the solution to cos x equals 3 cos x - 2?
1
What is Sin squared x - Cos squared x divided by 1 - Tan squared x equals cos squared x?
22
Sin A cos A plus 1 3sqrt3 4 How do you find the angle A?
The Answers.com interface does not handle symbols. Generally, algebraic expressions need to be written out with words like equals, plus, minus, multiplied by, divided by, etc.
Cos plus cos plus cos?
3cos
Who formulated eix equals cos x plus you sin x?
leonhard euler
How do you express sin x plus cos x divided by cos x in terms of tan x?
(sin x + cos x) / cosx = sin x / cos x + cosx / cos x = tan x + 1
How do you solve sinx divided by 1 plus cosx plus cosx divided by sinx?
sin x/(1+cos x) + cos x / sin x Multiply by sin x (1+cos x) =[(sin^2 x + cos x(1+cos x) ] / sin x (1+cos x) = [(sin^2 x + cos x + cos^2 x) ] / sin x (1+cos x) sin^2 x + cos^2 x = 1 = (1+cos x) / sin x (1+cos x) = 1/sin x
