Verified answer

i am reading your question as (sec x+ csc x)/(1+tan x)

start by using the defs: sec x = 1/cos x

csc x = 1/sin x(sinx +cosx)/(sinx cosx)

tan x = sinx/cosx

so the numerator becomes:

1/cos x + 1/ sin x = (sinx +cosx)/(sinx cosx) after adding fractions

the denominator becomes:

1+(sinx/cosx) = (cosx+sinx)/cosx

the fraction then becomes:

[(sinx +cosx)/(sinx cosx)]/[(cosx+Sinx)/cosx]

the common terms of (sinx+cosx) in both num and denom cancel, leaving:

cos x/(sinx cosx) = 1/sin x = csc x

?Explanation?: (sin x - a million) (tan x + sec x) improve: (sin x - a million) ((sin x / cos x) + (a million / cos x)) (sin x - a million) (sin x + a million / cos x) sin²x - a million / cos x factor out a unfavorable: -a million ( a million - sin²x ) / cos x keep in mind that "a million - sin²x" is comparable to cos²x -a million (cos²x) / cos x Simplify: -a million cos x / a million - cos x <--------answer :D