Question

(tgt+ctgt)^2-(tgt-ctgt)^2

Answer 1

(tgt+ctgt)^2-(tgt-ctgt)^2=tg^2t+2×tgt×ctgt+ctg^2t-tg^2t+2×tgt×ctgt-ctg^2t=4×tgt×ctgt=
4×sint/cost×cost/sint=4

Answer 2

Using the identity a^2 - b^2 = (a + b)(a - b), we can simplify the expression:

(tgt+ctgt)^2-(tgt-ctgt)^2 = [(tgt + ctgt) + (tgt - ctgt)] [(tgt + ctgt) - (tgt - ctgt)] = [2tgt][2ctgt] = 4tgt^2ctgt

Therefore, (tgt+ctgt)^2-(tgt-ctgt)^2 simplifies to 4tgt^2ctgt.