Question

PLEASE ANSWER this

If cotA + tanA = p and cotA – tanA = q, then the value of p^2-q^2 is

Answer 1

we have :-

cotA + tanA = p

cotA - tanA = q

To find :-

the value of p² - q²

basic information :-

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• cotA.tanA = 1/tanA×tanA = 1

Solution :-

(cotA + tanA)² - (cotA - tanA)²

= (cot²A + tan²A + 2cotA.tanA ) - ( cot²A +

tan²A - 2cotA.tanA)

= ( cot²A + tan²A ) - ( cot²A + tan²A )

= cot²A + tan²A + 2 - cot²A - tan²A + 2

{(+cot²A) cancelled by (-cotA) similarly

(+tanA) is cancelled by (-tanA)}

= 2 + 2

= 4

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