Question

If cosec A - cot A = q then the value of q^2 - 1/q^2+1 +cos a is
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Answer 1

Answer:

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Step-by-step explanation:

answer is 0

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Answer 2

Answer:

$\frac{q^2 - 1}{q^2+1} +cos A$  = 0

Step-by-step explanation:

Given,

cosec A - cot A = q

To find

$\frac{q^2 - 1}{q^2+1} +cos A$

Recall the formula

cosec²A - cot² A = 1

Solution:

q = cosec A -  cotA

q² = (cosec A - cot A)²

= cosec²A +cot²A - 2 cosecA cotA

q² - 1 = cosec²A +cot²A - 2 cosecA cotA - 1

= (cosec²A  - 1)+cot²A - 2 cosecA cotA

= cot²A + cot²A - 2 cosecA cotA

= 2cot²A - 2 cosecA cotA

= 2cotA(cotA - cosecA)

q² - 1 = 2cotA(cotA - cosecA)

q² + 1 = cosec²A +cot²A - 2 cosecA cotA + 1

=cosec²A +cosec²A - 2 cosecA cotA

= 2cosec²A - 2 cosecA cotA

= 2cosecA( cosec A - cotA)

= -2cosecA (cotA - cosecA)

q² + 1 =- 2cosecA( cot A - cosecA)

$\frac{q^2 - 1}{q^2+1} = \frac{2cotA(cotA - cosecA)}{-2cosec A( cot A - cosec A)}$

= $-\frac{cot A}{cosec A}$

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

= - cosA

$\frac{q^2 - 1}{q^2+1} +cos A$ = - cosA + cosA = 0

∴ $\frac{q^2 - 1}{q^2+1} +cos A$  = 0

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