Question

prove that:( cosA/cosecA+1 )+(cosA/cosecA-1)=2tanA
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Answer 1

Answer:

aagaya bhai.............

Answer 2

To Prove

$\sf\frac{cosA}{cosecA+1}+\frac{cosA}{cosecA-1}=2tanA$

Proof

Taking LHS,

$\sf\frac{cosA}{cosecA+1}+\frac{cosA}{cosecA-1}$

⇒ $\sf cosA(\frac{1}{cosecA+1}+ \frac{1}{cosecA-1})$

Taking LCM

⇒ $\sf cosA(\frac{cosecA-1+cosecA+1}{(cosecA+1)(cosecA-1)})$

Using (a +b)(a - b) = a² - b²

⇒ $\sf cosA(\frac{2cosecA}{cosec^2A-1})$

Using cosec²∅ - 1 = cot²∅, we get

⇒ $\sf cosA(\frac{2cosecA}{cot^2A})$

⇒ $\sf \frac{2cosA}{sinA}(\frac{1}{cot^2A})$ (since, cosecA = 1/sinA)

⇒ $\sf \frac{2cotA}{cot^2A}$

(since, cosA/sinA = cotA)

⇒ $\sf \frac{2}{cotA}$

⇒ $\sf 2 tanA$

(since, tanA = 1/cotA)

= RHS

Hence Proved