3. Evaluare \( \cos 75 \cos 45-\cos 15 \cos 45 \) cos \( 79 \sin 311+\sin 101 \sin 49 \) 3.2 Determine the value of \( \sin 3 x \cos y+\cos 3 x \sin y \) 3.3 Dftermine the value of \( x^{2}+y^{2} \) if \( x=2 \cos \theta\{y=2 \)

Calculate or simplify the expression \( \cos(75)\cos(45)-\cos(15)\cos(45) \). Calculate the value by following steps: - step0: Calculate: \(\cos\left(75\right)\cos\left(45\right)-\cos\left(15\right)\cos\left(45\right)\) - step1: Transform the expression: \(\frac{\cos\left(120\right)+\cos\left(30\right)}{2}-\cos\left(15\right)\cos\left(45\right)\) - step2: Transform the expression: \(\frac{\cos\left(120\right)+\cos\left(30\right)}{2}-\frac{\cos\left(60\right)+\cos\left(30\right)}{2}\) - step3: Transform the expression: \(\frac{\cos\left(120\right)+\cos\left(30\right)-\left(\cos\left(60\right)+\cos\left(30\right)\right)}{2}\) - step4: Calculate: \(\frac{\cos\left(120\right)-\cos\left(60\right)}{2}\) Calculate or simplify the expression \( \\cos(79)\\sin(311)+\\sin(101)\\sin(49) \). Calculate the value by following steps: - step0: Calculate: \(\cos\left(79\right)\sin\left(311\right)+\sin\left(101\right)\sin\left(49\right)\) - step1: Calculate the trigonometric value: \(-0.446954\) Calculate or simplify the expression \( \\sin(3x)\\cos(y)+\\cos(3x)\\sin(y) \). Simplify the expression by following steps: - step0: Solution: \(\sin\left(3x\right)\cos\left(y\right)+\cos\left(3x\right)\sin\left(y\right)\) - step1: Transform the expression: \(\sin\left(3x+y\right)\) Calculate or simplify the expression \( x^{2}+y^{2} \) when \( x=2\cos(\theta) \) and \( y=2 \). Simplify the expression by following steps: - step0: Solution: \(x^{2}+y^{2}\) The value of \( \cos(75) \cos(45) - \cos(15) \cos(45) \) is \( \frac{\cos(120) - \cos(60)}{2} \). The value of \( \cos(79) \sin(311) + \sin(101) \sin(49) \) is -0.446954. The value of \( \sin(3x) \cos(y) + \cos(3x) \sin(y) \) is \( \sin(3x+y) \). The value of \( x^{2} + y^{2} \) when \( x = 2\cos(\theta) \) and \( y = 2 \) is \( x^{2} + y^{2} \).