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2 years ago

Solve the quadratic equation by completing the square. =+x^2+16x +61=0

1 answer:

3 0

X^2 + 16x + 61 = 0
x^2 + 16x = -61
x^2 + 16x + 64 = -61 + 64
(x + 8)^2 = 3
x + 8 = (+-) sqrt 3
x = -8 (+-) sqrt 3

x = -8 + sqrt 3...and x = -8 - sqrt 3 <== ur solutions

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Show that √(1-cos A/1+cos A) =cosec A - cot A

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Hi there!

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We can begin by multiplying by its conjugate:

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Simplify using the identity:

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Take the square root of the expression:

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Multiply again by the conjugate to get a SINGLE term in the denominator:

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Simplify:

${\frac{sinA(1-cosA)}{1-cos^2A} =$

Use the above trig identity one more:

${\frac{sinA(1-cosA)}{sin^2A} =$

Cancel out sinA:

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Split the fraction into two:

${\frac{1}{sinA} - \frac{cosA}{sinA} =$

Recall:

$1/sinA = cscA\\\\cosA/sinA = cotA$

Simplify:

$\frac{1}{sinA} + \frac{cosA}{sinA} = \boxed{cscA - cotA}$

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