Learn how to solve factorization problems step by step online. Prove the trigonometric identity (sin(a)+cos(a))^2-tan(a)cos(a)^2=1+sin(a)cos(a). Starting from the left-hand side (LHS) of the identity. Apply trigonometric identities to simplify -\tan\left(a\right)\cos\left(a\right)^2 into \cos\left(a\right). Expand the expression \left(\sin\left(a\right)+\cos\left(a\right)\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Combining like terms 2\sin\left(a\right)\cos\left(a\right) and -\cos\left(a\right)\sin\left(a\right).

Prove the trigonometric identity (sin(a)+cos(a))^2-tan(a)cos(a)^2=1+sin(a)cos(a)