Question

Sin 210 cos150 + sin120 cos240​

Answer 1

Answer:

0

Step-by-step explanation:

To Find :-

sin210°.cos150° + sin120°.cos240°

How To Do :-

We need to convert the ratios in the form of quadrants like (90 - θ) , (180 + θ) like that , and after we need to simplify it by the quadrant formulas and then we need to substitute the value of them by using the trigonometric table.

Formula Required :-

In second quadrant [ (180 -  θ) , (90 +  θ) ] :-

'sin' ratio is positive

'cos' ratio is negative

In third quadrant [ (180 +  θ) , (270 -  θ) ] :-

'sin' ratio is negative

'cos' ratio is negative

sin30° = 1/2

sin60° = √3/2

cos30° = √3/2

cos60° = 1/2

Solution :-

sin210°.cos150° + sin120°.cos240°

We can write :-

210° = 180° + 30°

150° = 180° - 30°

120° = 180° - 60°

240° = 180° + 60°

Substituting these values :-

$=sin(180^{\circ}+30^{\circ}).cos(180^{\circ}-30^{\circ})+sin(180^{\circ}-60^{\circ}).cos(180^{\circ}+60^{\circ})$

$=-sin30^{\circ}\times (-cos30^{\circ})+sin60^{\circ}\times (-cos60^{\circ})$

Substituting the values :-

$=\left(-\dfrac{1}{2}\right)\left(-\dfrac{\sqrt{3}}{2}\right)+\left(\dfrac{\sqrt{3}}{2}\right)\left(-\dfrac{1}{2}\right)$

$=\dfrac{\sqrt{3}}{4}-\dfrac{\sqrt{3}}{4}$

= 0