Question

prove that:
cosecA/cosecA + 1 + cosecA/cosecA - 1 = 2sec^2A

Answer 1

Your question is a bit wrong it should be cosecA/cosecA - 1 + cosecA/cosecA - 1 = 2sec^2A
cscA /(cscA - 1 ) + cscA/(cscA + 1) 
 ⇒{cscA(cscA - 1) + cscA(cscA + 1)} / (cscA - 1)(cscA + 1) 
⇒ cscA(cscA - 1 + cscA + 1) / (cscA - 1)(cscA + 1) 
⇒ cscA( 2cscA ) / (csc²A - 1 ) 
⇒ 2csc²A / csc²A - 1 
⇒ 2/sin²A / (1/sin²A - 1 ) 
⇒ 2/sin²A / (1 - sin²A )/sin²A 
⇒ 2 / (1 - sin²A ) 
⇒ 2 / cos²A 
⇒ 2.sec²A

Answer 2

Answer:Here is Your answer....

Step-by-step explanation:

CosecA/CosecA-1 + CosecA/CosecA+1

Cosec^2A+CosecA+Cosec^2A-CosecA / Cosec^2A-1 ....... (((CROSS MULTIPLICATION)))

2Cosec^2A/Cosec^2A-1 ... (CosecA and -CosecA will be cancelled)

2Cosec^2A/Cot^2A ..... ((( COSEC^2A-1= Cot^2A)))

2×(1/sin^2A) / (cos^2A/Sin^2A).......

(((( cosec^2A=1/Sin^2A & cot^2A=cos^2A/sin^2A))))

2×1/Cos^2A .....( Sin^2A will be cancelled)))

2sec^2A......

Hope You Like My answer and Method...