Why is tan+cot=1/(sincos)

tan + cot
= (sin/cos) + (cos/sin)
= (sin^2)/(sin*cos) + (cos^2)/(sin*cos)
= (sin^2 + cos^2)/(sin*cos)
= 1/(sin*cos)

tanx + cotx =1/(sinxcosx)
trig identities:
sinx/cosx + cosx/sinx =
sin^2x + cos^2x/sinxcosx = (common denominator)
1/(sinxcosx) = 1/(sinxcosx) (sin^2x + cos^2x = 1)

tan+cot = tan + 1/tan=LHS

sin^2+cos^2/sin.cos = RHS
sin/cos + cos/sin = RHS
tan + 1/tan = RHS
LHS = RHS

sinΘ/cosΘ + cosΘ/sinΘ = (sin²Θ + cos²Θ)/sinΘcosΘ = 1/(sinΘcosΘ)

Which also equals secΘcscΘ

both r absolutely right.

joker is right!