(1/cos^2 15+1/sin^2 15)

Răspuns :

[tex]\dfrac{1}{cos^215^{\circ}}+\dfrac{1}{sin^215^{\circ}}=\dfrac{sin^215+cos^215}{sin^215cos^215}=\dfrac{1}{(sin15cos15)^2}=[/tex]

[tex]=\dfrac{4}{(2sin15cos15)^2}= \dfrac{4}{sin^230}=\dfrac{4}{\dfrac14}=16.[/tex]

Am folosit formula fundamentala a trigonometriei>

[tex]sin^2x+cos^2x=1, \forall x[/tex]
Am folosit si formula [tex]2sinx\cdot cosx=sin2x[/tex]