Question

Stiind ca sin (x) = $\frac{4}{5}$ si cos (y) = $\frac{3}{5}$ ; x,y ∈(0,$\frac{\pi }{2}$) sa se calculeze cos (x) + sin (y)

Answer 1

$\displaystyle x, y\in\left(0, \frac\pi2\right)\Rightarrow \sin x\geq0, \:\cos x\geq0,\:\sin y\geq0,\:\cos y\geq0\\\sin^2x+\cos^2x=1\Rightarrow \cos^2x=1-\sin^2x=1-\frac{16}{25}=\frac{9}{25}\Rightarrow |\cos x|=\frac35\\\text{Cum }\cos x\geq0\Rightarrow \cos x = \frac35\\\sin^2y+\cos^2y=1\Rrightarrow\sin^2y=1-\cos^2y=1-\frac{9}{25}=\frac{16}{25}\Rightarrow|\sin y|=\frac45\\\text{Cum }\sin y\geq0\Rightarrow \sin y = \frac45\\\cos x+\sin y=\frac35+\frac45=\frac75$