Question

Evaluate Sin2 19 + sin2 71

Answer 1

sin^2(19)+sin^2(71)
=sin^(19)+sin^2(90-19)
=sin^2(19)+cos^219
=1

Answer 2

$\bold{ { \sin(19) }^{2} + { \sin(71) }^{2} }\\ \\ \\ \\ \bold{identities \: of \: trigonometry : }\\ \\ \bold{{\sin(\theta) }^{2} + { \cos(\theta) }^{2} = 1} \\ \\ \bold{{ \sin(\theta) }= { \cos(90 - \theta)}}$$\bold{ by \: using \: second \: formula : }\\ \\ \bold{{ \sin(71) } = \cos(90 - 71)} \\ \\ \bold{\sin(71) = \cos(19) }\\ \\ \\ \\ \bold{use \: this \: in \: equation : }$$\bold{{ \sin(19) }^{2} + { \sin(71) }^{2} }\\ \\ \bold{{ \sin(19) }^{2} + { \cos(19) }^{2} }\\ \\ \\ \\ \bold{by \: using \: first \: identity :} \\ \\\bold{ { \sin(19) }^{2} + { \cos(19) }^{2} = 1 \\ \\ }$