Question

If tan¥=4/5,then (1-cos¥)/(1+cos¥)is

Answer 1

Hi ,

tan¥ = 4/5 ----( 1 )

sec²¥ = 1 + tan²¥

= 1 + ( 4/5 )²

= 1 + 16 / 25

= ( 25 + 16 ) / 25

= 41 / 25

sec¥ = √ ( 41 / 25 ) = √41 / 5

1 / cos¥ = √41 / 5

cos¥ = 5/ √41 ----( 2 )

Now ,

( 1 - cos¥ ) / ( 1 + cos¥ )

= ( 1 - 5 / √41 ) / ( 1 + 5 / √41 )

= ( √41 - 5 ) / ( √41 + 5 )

= ( √41 - 5 )( √41 - 5 ) / ( √41 + 5 ) ( √41 - 5 )

= ( √41 - 5 )² / [ (√41 )² - 5² ]

= ( 41 + 25 - 2 × √41 × 5 ) / ( 41 - 25 )

= ( 66 - 10√41 ) / 16

= 2 ( 33 - 5√41 ) / 16

= ( 33 - 5√41 ) / 8

I hope this helps you.

:)