Question

Show that √[(1 + sin A) / (1 − sin A) ]= sec A + tan A

Answer 1

Hi ,

LHS = √ ( 1 + sinA )/( 1 - sinA )

= √[(1 + sinA)(1 + sinA)/(1 - sinA)(1 + sinA)]

= √ ( 1 + sinA )² / ( 1² - sin²A )

= √ ( 1 + sinA )² /( 1 - sin² A )

= √ ( 1 + sinA )² / cos² A

= ( 1 + sinA )/cosA

= 1/cosA + sinA/cosA

= secA + tanA

= RHS

I hope this helps you.

: )