Question

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

Answer 1

$\dfrac{1}{cos^215^{\circ}}+\dfrac{1}{sin^215^{\circ}}=\dfrac{sin^215+cos^215}{sin^215cos^215}=\dfrac{1}{(sin15cos15)^2}=$

$=\dfrac{4}{(2sin15cos15)^2}= \dfrac{4}{sin^230}=\dfrac{4}{\dfrac14}=16.$

Am folosit formula fundamentala a trigonometriei>

$sin^2x+cos^2x=1, \forall x$
Am folosit si formula $2sinx\cdot cosx=sin2x$