$\left(\sin\left(x\right)+\cos\left(x\right)\right)^2$
$1+cot^2x$
$tan\left(x\right)csc\left(x\right)$
$\tan\left(x\right)\csc\left(x\right)$
$\frac{2+\tan^2\left(x\right)}{\sec^2\left(x\right)}-1$
$csc^2x-1$
Special products is the multiplication of algebraic expressions that follow certain rules and patterns, so you can predict the result without necessarily doing the multiplication.
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