Trigonometric questions

Question

What is the value of sec x - tanx if escx + cot x = 2

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Answer 1

if it is meant to ask what is value of f(x)=sec(x)-tan(x)

if 2=csc(x)+cot(x) is given

then x=sin^-1(1/√5)-tan^-1(-1/2),,,,corrected removed parenthesis signs

and value of f(x)=1/3

method is to use given

and find (√5)(sin(x+tan^-1(-1/2))=1

this finds x

use algebra and trig addition formulas, and decomposition of sin(tan¹(-1/2), cos(sin^-1(1/√5)), etc.

to find f(x)=1/3 at x value found