sec x tan xcsc x 1 cot xSolutionsecx tanxcscx 1 cotx LH

(sec x - tan x)(csc x + 1) = cot x

(secx - tanx)(cscx +1) = cotx

LHS : secx*cscx + secx - tanxcscx - tanx

1/sinxcosx + 1/cosx - sinx/cosx*sinx - tanx

1/sinxcosx +1/cosx - 1/cosx - tanx

1/sinxcosx - sinx/cosx

(1 -sin^2x)/cosxsinx

cos^2x/cosxsinx

cosx/sinx

cotx

RHS