Learn how to solve problems step by step online. Prove (1+cos(x))/2+(-sin(x))/(2tan(x))=1/2. Starting from the left-hand side (LHS) of the identity. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Divide fractions \frac{-\sin\left(x\right)}{\frac{2\sin\left(x\right)}{\cos\left(x\right)}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Simplify the fraction \frac{-\sin\left(x\right)\cos\left(x\right)}{2\sin\left(x\right)} by \sin\left(x\right).

Prove (1+cos(x))/2+(-sin(x))/(2tan(x))=1/2