secBcscBxcosBsinB cotBtanB show as an identitySolution sec b

(secB+cscB)x(cosB-sinB)= cotB-tanB show as an identity.

Solution

( sec b + csc b) * ( cos b - sin b ) = cot b - tan b

proving the left hand side

sec b = 1/ cos b

csc b = 1/ sin b

( 1/ cos b + 1/ sin b ) ( cos b - sin b)

(sin b + cos b) /( cos b sin b) ( cos b - sin b)

( cos^b - sin^2 b ) / (cos b sin b )

cos^2b / ( cos b sin b ) = cot b

sin^2 b / cos b sin b = tan b

hence we get

cot b - tan b   which is right hand side

proved !