Match the following show work to support your answer a 1 b c

Match the following (show work to support your answer): (a) -1 (b) cos x (c) cot x (d) csc x (e) sec^2 x + tan^2 x (f) 1 (g) - tan x (h) sin x (i) sec^2 x (j) sin^2 x ______ secx cosx ______sin(-x)/cos (-x) ______tan^2x - sec^2 x ______ 1-cos^2x/sinx ______cot x sin x ______cos^2x (sec^2 x - 1) ______sec^2 x - 1/sin^2 x ______ sec^4 x - tan^4x ______cos x cot x + sin x

Solution

( f ) = secx cosx = (1/cosx)*cosx = 1

( g ) = sin(-x)/cos(-x) = -sinx/cosx = -tanx

( a ) = tan²x-sec²x = tan²x-(1+tan²x) = -1

( h ) = (1-cos²x)/sinx = sin²x/sinx = sinx

( b ) = ctsxsinx = (cosx/sinx)*sinx = cosx

( j ) = cos²x(sec²x-1) = cos²x(tan²x) = cos²x(sin²x/cos²x) = sin²x

( i ) = (sec²x-1)/sin²x = tan²x/sin²x = 1/cos²x = sec²x

( e ) = sec⁴x - tan⁴x = (sec²x - tan²x)(sec²x + tan²x) = (1)(sec²x + tan²x)

( d ) = cosxcotx+sinx = cosx (cosx/sinx) + sinx = (cos²x+sin²x)/sinx 1/sinx = cscx