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 $$ x=2 \cos heta\{y=2 $$

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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 $$ x=2 \cos 	heta\{y=2 $$

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Calculate or simplify the expression $$ \cos(75)\cos(45)-\cos(15)\cos(45) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\cos\left(75ight)\cos\left(45ight)-\cos\left(15ight)\cos\left(45ight)$$
- step1: Transform the expression:
  $$\frac{\cos\left(120ight)+\cos\left(30ight)}{2}-\cos\left(15ight)\cos\left(45ight)$$
- step2: Transform the expression:
  $$\frac{\cos\left(120ight)+\cos\left(30ight)}{2}-\frac{\cos\left(60ight)+\cos\left(30ight)}{2}$$
- step3: Transform the expression:
  $$\frac{\cos\left(120ight)+\cos\left(30ight)-\left(\cos\left(60ight)+\cos\left(30ight)ight)}{2}$$
- step4: Calculate:
  $$\frac{\cos\left(120ight)-\cos\left(60ight)}{2}$$
Calculate or simplify the expression $$ \cos(79)\sin(311)+\sin(101)\sin(49) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\cos\left(79ight)\sin\left(311ight)+\sin\left(101ight)\sin\left(49ight)$$
- 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:
  $$\sin\left(3xight)\cos\left(yight)+\cos\left(3xight)\sin\left(yight)$$
- step1: Transform the expression:
  $$\sin\left(3x+yight)$$
Calculate or simplify the expression $$ x^{2}+y^{2} $$ when $$ x=2\cos(	heta) $$ 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 $$ x = 2\cos(	heta) $$ and $$ y = 2 $$ is $$ x^{2} + y^{2} $$.
Calculate the following expressions: 1. $$ \cos(75) \cos(45) - \cos(15) \cos(45) $$ 2. $$ \cos(79) \sin(311) + \sin(101) \sin(49) $$ 3. $$ \sin(3x) \cos(y) + \cos(3x) \sin(y) $$ 4. $$ x^{2} + y^{2} $$ where $$ x = 2\cos(	heta) $$ and $$ y = 2 $$ Solutions: 1. $$ \cos(75) \cos(45) - \cos(15) \cos(45) = \frac{\cos(120) - \cos(60)}{2} $$ 2. $$ \cos(79) \sin(311) + \sin(101) \sin(49) = -0.446954 $$ 3. $$ \sin(3x) \cos(y) + \cos(3x) \sin(y) = \sin(3x + y) $$ 4. $$ x^{2} + y^{2} = (2\cos(	heta))^{2} + 2^{2} = 4\cos^{2}(	heta) + 4 $$

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 \( x=2 \cos \theta\{y=2 \)

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