Question

Упростить 1)sin 15' *cos 30' + sin 15'*cos 30' 2)sin 70' cos 40' - sin 40' cos 70'  

Answer 1

1)sin 15' *cos 30' + sin 15'*cos 30'

 

)sin(15+30)=45

sin45=$\sqrt{2}$

             --------------------

                         2

 

2)sin 70' cos 40' - sin 40' cos 70'=

 

 

)sin(70-40)=30

sin30=1/2

 я применла формулу

sin(α + β) = sin α cos β + cos α sin β 

и точно также со знаком минус

Answer 2

1. Let's simplify the expression:

sin 15' * cos 30' + sin 15' * cos 30'

Using the identity: sin(A + B) = sin A * cos B + cos A * sin B, we can rewrite the expression as:

2 * sin 15' * cos 30'

Now, we need to evaluate the trigonometric values of 15' and 30'. Using the values from the unit circle:

sin 15' = 1/4 cos 30' = √3/2

Substituting these values into the expression:

2 * (1/4) * (√3/2) = √3/4

Therefore, the simplified expression is √3/4.

2. Let's simplify the expression:

sin 70' * cos 40' - sin 40' * cos 70'

Using the identity: sin(A - B) = sin A * cos B - cos A * sin B, we can rewrite the expression as:

sin 70' * cos 40' - sin 40' * cos 70'

Now, we need to evaluate the trigonometric values of 40' and 70'. Using the values from the unit circle:

sin 40' = √3/4 cos 70' = 1/√2

Substituting these values into the expression:

(√3/4) * (1/√2) - (√3/4) * (1/√2) = 0

Therefore, the simplified expression is 0.