Question

prove that √cosecA+1/cosecA-1=1+sinA/cosA
10th standard state board students only answer Karnataka ​

Answer 1

Step-by-step explanation:

(cosecA-1)/(cosecA+1)

=(1/sinA-1)/(1/sinA+1)

=(1-sinA/sinA)/(1+sinA/sinA)

=1-sinA/1+sinA

Multiply the numerator and denominator by (1+sinA)

=(1-sinA)(1+sinA)/(1+sinA)(1+sinA)

=1-sinA²/1+sin²A

=cos²A/1+sin²A

= 1+sinA/cosA

Hence proved...

Answer 2

Answer:

LHS:

Root of CosecA+1/CosecA-1 X CosecA+1/ CosecA+1   [Rationalizing the denominator]

Root of (CosecA+1)^/ Cosec^A-1

Root of (CosecA+1)^/ cot^A

CosecA+1/ CotA

1/SinA+1/ cosA/sinA

1+ sinA/sinA/ CosA/sinA

1+sinA/cosA

Hence proved.