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.
2 cos * cos * -1 = 2cos(square) * -1 =cos(square) + cos(square) *-1 =1- sin(square) +cos(square) * -1 1 - 1 * -1 =0
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.
How is it possible that the value of cosecant is less than 1 (2/7)?
There is a hint to how to solve this in what is required to be shown: a and b are both squared.Ifa cos θ + b sin θ = 8a sin θ - b cos θ = 5then square both sides of each to get:a² cos² θ + 2ab cos θ sin θ + b² sin² θ = 64a² sin² θ - 2ab sin θ cos θ + b² cos² θ = 25Now add the two together:a² cos² θ + a² sin² θ + b² sin² θ + b² cos² θ = 89→ a²(cos² θ + sin² θ) + b² (sin² θ + cos² θ) = 89using cos² θ + sin² θ = 1→ a² + b² = 89
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.
[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,
1. Anything divided by itself always equals 1.
Until an "equals" sign shows up somewhere in the expression, there's nothing to prove.
No, but cos(-x) = cos(x), because the cosine function is an even function.
Sin 15 + cos 105 = -1.9045
1
2 cos * cos * -1 = 2cos(square) * -1 =cos(square) + cos(square) *-1 =1- sin(square) +cos(square) * -1 1 - 1 * -1 =0
22
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3cos
leonhard euler
(sin x + cos x) / cosx = sin x / cos x + cosx / cos x = tan x + 1