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Take a right angled triangle ABC with the right angle at B, so that AC is the hypotenuse.
Let AC be 1 unit long.
Using the angle CAB, the length of AC and the trigonometric ratios:
sin = opposite/hypotenuse ⇒ sin CAB = AB/AC = AB/1 = AB
cos = adjacent/hypotenuse ⇒ cos CAB = BC/AC = BC/1 = BC
Using Pythagoras:
AB2 + BC2 = AC2
⇒ (sin CAB)2 + (cos CAB)2 = 12
⇒ sin2θ + cos2θ = 1
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What is cos theta minus cos theta times sin squared theta?
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What is sec squared theta minus tan squared theta?
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How do you solve csc x sin x equals cos x cot x plus?
Suppose csc(x)*sin(x) = cos(x)*cot(x) + y then, ince csc(x) = 1/sin(x), and cot(x) = cos(x)/sin(x), 1 = cos(x)*cos(x)/sin(x) + y so y = 1 - cos2(x)/sin(x) = 1 - [1 - sin2(x)]/sin(x) = [sin2(x) + sin(x) - 1]/sin(x)
What is cos if csc -9?
Cosec = -9 => sin = -1/9 Then, cos2 = 1 - sin2 = 1 - (-1/9)2 = 1 - 1/81 = 80/81 and so cos = sqrt(80/81) = ±8.94/9 = ±0.99
What is the solution to cos2 plus cos2tan2 equals 1?
cos2 + cos2tan2 = cos2 + cos2*sin2/cos2 = cos2 + sin2 which is identically equal to 1. So the solution is all angles.
How does 1-sin squared x times 1 plus tan suared x equals 1?
Use these identities: sin2(x) + cos2(x) = 1, and tan(x) = sin(x)/cos(x) For clarity, the functions are written here without their arguments (the "of x" part). (1 - sin2) = cos2 (1 + tan2) = (1 + sin2/cos2) = (cos2+sin2) / cos2 = 1/cos2 Multiply them: (cos2) times (1/cos2) = 1'QED'
Sec²x - tan²x equals?
sec2(x) - tan2(x)= 1/cos2(x) - sin2(x)/cos2(x)= (1 - sin2(x)) / cos2(x)= cos2(x) / cos2(x)= 1
In maths does one minus two sine squared an equal cos squared a minus sine squared a 1-2sin2an equals sin2a-cos2a?
No.Remember: sin2 + cos2 = 1So, in place of (1 - 2 sin2) we can write (sin2 + cos2 - 2 sin2).Massage that around slightly: (sin2 + cos2 - 2 sin2) = cos2 - sin2That's not equal to (sin2 - cos2), which is the original question we were asked.
What is sin squared minus 1?
-cos2(x)1 = sin2(x) +cos2(x)1 - cos2(x) = sin2(x)-cos2(x) = sin2(x) - 1
What does negative sine squared plus cosine squared equal?
To determine what negative sine squared plus cosine squared is equal to, start with the primary trigonometric identity, which is based on the pythagorean theorem...sin2(theta) + cos2(theta) = 1... and then solve for the question...cos2(theta) = 1 - sin2(theta)2 cos2(theta) = 1 - sin2(theta) + cos2(theta)2 cos2(theta) - 1 = - sin2(theta) + cos2(theta)
How would you solve and show work for cos2 theta if cos squared theta equals 1 and theta is in the 4th quadrant?
cos2(theta) = 1 cos2(theta) + sin2(theta) = 1 so sin2(theta) = 0 cos(2*theta) = cos2(theta) - sin2(theta) = 1 - 0 = 1
1-2sin squared x equals?
3
Sine plus cosine equals?
There is no real significance to sine plus cosine, now sin2(x) + cos2(x) = 1 for any x, where sin2(x) means to take the sign of the number, then square that value.
How can you prove that 1-2 cosine squared over sine times cosine is equal to tangent minus cotangent?
sin2 + cos2 = 1 So, (1 - 2*cos2)/(sin*cos) = (sin2 + cos2 - 2*cos2)/(sin*cos) = (sin2 - cos2)/(sin*cos) = sin2/(sin*cos) - cos2/(sin*cos) = sin/cos - cos-sin = tan - cot
How can you write an expression for cos x in term of sin x using pythagorean theorem?
cos2 x + sin2 x = 1 cos2 x = 1 - sin2 x
How does sec-squared x equals 1 plus tan-squared x?
Let s = sin x; c = cos x. By definition, sec x = 1/cos x = 1/c; and tan x = (sin x) / (cos x) = s/c. We know, also, that s2 + c2 = 1. Then, dividing through by c2, we have, (s2/c2) + 1 = (1/c2), or (s/c)2 + 1 = (1/c)2; in other words, we have, tan2 x + 1 = sec2 x.
