Question

Evaluate sin30 cos 45 - sin30 sin 45

Answer 1

To evaluate,

sin30 cos 45 - sin30 sin45

We know,

sin 30 = $\frac{1}{2}$

cos 45 =$\frac{1}{2\sqrt{2}}$

sin 45 = $\frac{1}{2\sqrt{2}}$

All these values are taken from trigonometric table.
All these angles are standard angles.

Main part :

sin 30 cos 45 - sin 30 sin 45

Substituting the values that we know , we get :-

$( \frac{1}{2} \times \frac{1}{ \sqrt{2} } ) - ( \frac{1}{2} \times \frac{1}{ \sqrt{2} } )$
$( \frac{1}{ {2}^{1 + \frac{1}{2} } } ) - ( \frac{1}{ {2}^{1 + \frac{1}{2} } } )$
$( \frac{1}{ {2}^{ \frac{3}{2} } } ) - ( \frac{1}{ {2}^{ \frac{3}{2} } } )$
$( \frac{1}{2 \sqrt{2} } ) -( \frac{1}{2 \sqrt{2} } )$
LCM = 2√2

$\frac{1 - 1}{2 \sqrt{2} }$
$\frac{0}{2 \sqrt{2} }$
Anything divided by zero is equal to 0.

$0$
Answer :- 0

Answer 2

Hey there!

Given trigonometric equation here,

$\bf{sin{(30)} cos{(45)} - sin{(30)} sin{(45)}}$

Now, implying the use of the following trigonometric identity rule for "sin" that is,

$\bf{cos{(x)} = sin{(90 - x)}}$

And, the trigonometric identity rule for the function for "sin" and adding the value to it, that is,

$\bf{cos{(45)} = sin{(90 - 45)}}$

Put these trigonometric identities for their respective trigonometric functions into our equation to obtain and evaluate the final answer or a value for it,

$\bf{= sin{(30)} sin{(90 - 45)} - sin{(30)} sin{(45)}}$

$\bf{= sin{(30)} sin{(45)} - sin{(30)} sin{(45)}}$

Now, just add those similar elements to get the final answers and to complete this evaluation.

$\bf{0}$

Which is the required solution for these types of queries.

Hope this helps.