Sec x csc xtan x cos x sin x cos x sin x cos xsec x cs

Sec x + csc x/tan x + cos x = sin x + cos x sin x + cos x/sec x + csc x = sin x cos x tan^2 n - sin^2 U = tan^2 U sin^2 u 1/sec x + tan x + 1/sec x -= tan x = 2 sec cos^2t + tan^2 t - 1/sin^2 t = tan^2 t

Solution

1) ( sin x + cos x ) / ( sec x + csc x )

sec x = 1 / cos x

csc x = 1 / sin x

( sin x + cos x ) / ( 1 / cos x + 1 / sin x )

( sin x + cos x ) / ( sin x + cos x / ( cos x sin x )

cancelling like factors from top and bottom

= cos x sin x ( which is right hand side )

proved !