Question

se se calculeze $sin^2135+cos^245$ si sa se determine x ∈ (0;$\frac{\pi }{2}$)
stiind ca $\frac{tgx+2ctgx}{ctgx}=3$

Answer 1

sin180 = sin( 180 + 45) = - cos45 
sin²135 + cos²45 = ( -cos45)² + cos²45 = cos²45 + cos²45 = 2cos²45 = 
=2 ·(√2/2) ² = 2 · 2 / 4 = 1 
daca x∈( 0 , π/2) 
tgx + 2ctgx = 3ctgx 
tgx = ctgx           daca x∈ ( 0 ,π/2)   atunci x = π/4