Question

determinati x∈(0, π/2) pentru care cosx · sin( π/2 - x) - sinx · cos(π/2 - x) = 1/2

Answer 1

x∈(0, π/2);

cosx • sin( π/2 - x) - sinx • cos(π/2 - x) = 1/2

sin( π/2 - x)=cosx si cos(π/2 - x)=sinx

cosx • sin( π/2 - x) - sinx • cos(π/2 - x)=cosx•cosx-sinx•sinx

cos²x-sin²x=1/2

sin²x=1-cos²x

=> cos²x-1+cos²x=1/2

2cos²x=1/2+1

2cos²x=3/2

cos²x=3/4; x∈(0, π/2);

=> cosx=√(3/4)= √3 /2

=> x= π/6