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How do you prove that (1 plus cotx)2-2cotx 1(1-cos)(1 plus cos)?
Wiki User
∙ 6y ago
Manipulate normally, noting:
- cot x = cos x / sin x
- cos² x + sin² x = 1 → sin²x = 1 - cos² x
- a² - b² = (a + b)(a - b)
- 1 = 1²
- ab = ba
- a/(bc) = a/b/c
(1 + cot x)² - 2 cot x = 1² + 2 cot x + cot² x - 2 cot x
= 1 + cot² x
= 1 + (cos x / sin x)²
= 1 + cos² x / sin² x
= 1 + cos² x / (1 - cos² x)
= ((1 - cos² x) + cos² x)/(1 - cos² x)
= 1/(1² - cos² x)
= 1/((1 + cos x)(1 - cos x))
= 1/(1 - cos x)/(1 + cos x)
QED.
Wiki User
∙ 6y ago
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Cos plus cos plus cos?
3cos
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.
Why does sin plus cos equal one?
There is no reason at all. For most angles sin plus cos do not equal one.
Sin 15 plus cos 105 equals?
Sin 15 + cos 105 = -1.9045
Cos plus cos plus cos?
3cos
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.
How would you prove left cosA plus sinA right times left cos2A plus sin2A right equals cosA plus sin3A?
You need to make use of the formulae for sin(A+B) and cos(A+B), and that cos is an even function: sin(A+B) = cos A sin B + sin A cos B cos(A+B) = cos A cos B - sin A sin B cos even fn → cos(-x) = cos(x) To prove: (cos A + sin A)(cos 2A + sin 2A) = cos A + sin 3A The steps are to work with the left hand side, expand the brackets, collect [useful] terms together, apply A+B formula above (backwards) and apply even nature of cos function: (cos A + sin A)(cos 2A + sin 2A) = cos A cos 2A + cos A sin 2A + sin A cos 2A + sin A sin 2A = (cos A cos 2A + sin A sin 2A) + (cos A sin 2A + sin A cos 2A) = cos(A - 2A) + sin(A + 2A) = cos(-A) + sin 3A = cos A + sin 3A which is the right hand side as required.
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,
2 cos x plus 1 cos x plus -1 equals 0?
2 cos * cos * -1 = 2cos(square) * -1 =cos(square) + cos(square) *-1 =1- sin(square) +cos(square) * -1 1 - 1 * -1 =0
Cos x equals -cos x plus 1?
No, but cos(-x) = cos(x), because the cosine function is an even function.
Why does sin plus cos equal one?
There is no reason at all. For most angles sin plus cos do not equal one.
Prove that sin A cos A2?
Not correct. sin2alpha + cos2alpha = 1
What is the value of sin A plus cos Acos A (1-cos A) when tan A 815?
When tan A = 815, sin A = 0.9999992 and cos A = 0.0012270 so that sin A + cos A*cos A*(1-cos A) = 1.00000075, approx.
Factor sin cubed plus cos cubed?
sin cubed + cos cubed (sin + cos)( sin squared - sin.cos + cos squared) (sin + cos)(1 + sin.cos)
How do you prove this trigonometric relationship sin3A equals 3sinA cos 2 A - sin 3 A?
sin(3A) = sin(2A + A) = sin(2A)*cos(A) + cos(2A)*sin(A)= sin(A+A)*cos(A) + cos(A+A)*sin(A) = 2*sin(A)*cos(A)*cos(A) + {cos^2(A) - sin^2(A)}*sin(A) = 2*sin(A)*cos^2(A) + sin(a)*cos^2(A) - sin^3(A) = 3*sin(A)*cos^2(A) - sin^3(A)
Sin 15 plus cos 105 equals?
Sin 15 + cos 105 = -1.9045
