Question

1. scriind pi/2=pi/3-pi/4(sau 15grade=60grade-45 grade),verificati:
sin π/2=sin 15grade=√6-√2 totul pe 4
cos π/12=cos 15 grade=√6+√2 totul pe 4

2.caculati: cos 7π/12, sin 7π/12, cos 11π/12, sin 11π/12

3.calculati: a) sin10gradecos20grade+sin20gradecos10grade
b)cos19gradecos11grade-sin19gradesin11grade

4.calculati:
a)cos(x-y),daca x,y∈(0,π/2)si cosx=1/7,cos y=13/14
b)cos(π/3-a),daca a∈(3π/2,2π) si sin a=-12/13
c)sin(a-b) daca a∈(0,π/2),b∈(3π/2,2π) si sin a=√2/2,sin b=√2-√6 totul pe 4.

Answer 1

1) sin 15=sin(45-30)=sin45*cos30-sin30*cos45 (si iti da rez ala)
cos(45-30)=cos45*cos30+sin45*sin45
4)cos(x-y)
cosx=1/7
sin^2x+cos^2x=1=> sin^2x+1/49=1 => si^2x=1-1/49 =>sin^2x=49-1/49 => sin^2=48/49=> sinx=4√3/7

cosy=13/14
sin^2y+cos^2y=1 => sin^2y=196-169/196 => sin^2y=30/196 =.> siny=√30/14

Si acum poti calcula cos(x-Y)
Si la fel faci si la celelalte subpuncte