H5 \( =R H_{5} \) \[ \sin ^{2} \theta \] \( \sin \left(180^{\circ}-\theta\right) \cos \left(90^{\circ}+\theta\right)+\tan 45^{\circ} \)

Simplify the expression by following steps: - step0: Solution: \(\sin^{2}\left(\theta \right)\) Calculate or simplify the expression \( \sin(180 - \theta) * \cos(90 + \theta) + \tan(45) \). Simplify the expression by following steps: - step0: Solution: \(\sin\left(180-\theta \right)\cos\left(90+\theta \right)+\tan\left(45\right)\) - step1: Rewrite the expression: \(\sin\left(180-\theta \right)\cos\left(\theta +90\right)+\tan\left(45\right)\) - step2: Rewrite the expression: \(\cos\left(\theta +90\right)\sin\left(180-\theta \right)+\tan\left(45\right)\) Let's break down the expressions step by step. 1. **Expression 1:** \[ \sin(180^{\circ} - \theta) \cos(90^{\circ} + \theta) + \tan(45^{\circ}) \] - We know that: - \(\sin(180^{\circ} - \theta) = \sin(\theta)\) - \(\cos(90^{\circ} + \theta) = -\sin(\theta)\) - \(\tan(45^{\circ}) = 1\) Substituting these values into the expression gives: \[ \sin(\theta)(-\sin(\theta)) + 1 = -\sin^{2}(\theta) + 1 \] Therefore, the simplified form of the first expression is: \[ 1 - \sin^{2}(\theta) \] 2. **Expression 2:** \[ \sin^{2}(\theta) \] This expression is already in its simplest form. In summary: - The first expression simplifies to \(1 - \sin^{2}(\theta)\). - The second expression is \(\sin^{2}(\theta)\).