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Trava [24]
2 years ago
13

Lim x tends to π÷2 , then what is the value of (tanx + cotx) ÷ ( tanx - cotx)​

Mathematics
1 answer:
KiRa [710]2 years ago
8 0

(tan(<em>x</em>) + cot(<em>x</em>)) / (tan(<em>x</em>) - cot(<em>x</em>)) = (tan²(<em>x</em>) + 1) / (tan²(<em>x</em>) - 1)

… = (sin²(<em>x</em>) + cos²(<em>x</em>)) / (sin²(<em>x</em>) - cos²(<em>x</em>))

… = -1/cos(2<em>x</em>)

Then as <em>x</em> approaches <em>π</em>/2, the limit is -1/cos(2•<em>π</em>/2) = -sec(<em>π</em>) = 1.

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Step-by-step explanation:

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5 0
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Simplifying
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Reorder the terms:
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Reorder the terms:
-11 + 7x = 5(-2 + x) + 2x + -1
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Combine like terms: -10 + -1 = -11
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Combine like terms: 5x + 2x = 7x
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Add '11' to each side of the equation.
-11 + 11 + 7x = -11 + 11 + 7x

Combine like terms: -11 + 11 = 0
0 + 7x = -11 + 11 + 7x
7x = -11 + 11 + 7x

Combine like terms: -11 + 11 = 0
7x = 0 + 7x
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Add '-7x' to each side of the equation.
7x + -7x = 7x + -7x

Combine like terms: 7x + -7x = 0
0 = 7x + -7x

Combine like terms: 7x + -7x = 0
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Solving
0 = 0

3 0
3 years ago
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6 0
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6 0
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3 0
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