frac{1}{sin alpha }- cos alpha *ctg alpha = b) cos alpha +cos alpha * tg^{2} alpha = c) sin alpha +cos alpha *ctg alpha = d) (cos alpha +tg alpha *sin alpha )*ctg alpha =

a) [latex] frac{1}{sin alpha }- cos alpha *ctg alpha = [/latex] [latex] frac{1}{sin alpha } - cos alpha * frac{cos alpha}{sin alpha} = [/latex] [latex] frac{1}{sin alpha} - frac{cos^{2} alpha }{sin alpha} = [/latex] [latex]frac{1 - cos^{2} alpha }{sin alpha} = frac{sin^{2} alpha}{sin alpha} = sin alpha [/latex] b) [latex]cos alpha +cos alpha * tg^{2} alpha = cos alpha + cos alpha * frac{sin^{2} alpha}{cos^{2} alpha} = [/latex] [latex]frac{cos^{2} alpha}{cos alpha} + frac{sin^{2} alpha}{cos alpha} = [/latex] [latex]frac{cos^{2} alpha + sin^{2} alpha}{cos alpha} = frac{1}{cos alpha} [/latex] c) [latex]sin alpha +cos alpha *ctg alpha = [/latex] [latex]sin alpha + cos alpha * frac{cos alpha}{sin alpha} = [/latex] [latex]frac{sin^{2} alpha}{sin alpha} + frac{cos^{2} alpha}{sin alpha}=[/latex] [latex]frac{sin^{2} alpha + cos^{2} alpha}{sin alpha} = frac{1}{sin alpha}[/latex] d) [latex](cos alpha +tg alpha *sin alpha )*ctg alpha =[/latex] [latex](frac{cos^{2} alpha}{cos alpha} + frac{sin alpha}{cos alpha} * sin alpha) * frac{cos alpha}{sin alpha} = [/latex] [latex]frac{cos^{2} alpha + sin^{2} alpha}{cos alpha} * frac{cos alpha}{sin alpha} = [/latex] [latex]frac{1}{cos alpha} * frac{cos alpha}{sin alpha} = frac{1}{sin alpha}[/latex]

Sprawdź tożsamości: [latex] frac{1-cos alpha }{sin alpha } * frac{1+cos alpha }{cos alpha } = tg alpha \ frac{1-sin alpha }{sin alpha } * frac{1+sin alpha }{cos alpha } = ctg alpha [/latex]

Sprawdź tożsamości: [latex] frac{1-cos alpha }{sin alpha } * frac{1+cos alpha }{cos alpha } = tg alpha \ frac{1-sin alpha }{sin alpha } * frac{1+sin alpha }{cos alpha } = ctg alpha [/latex]...

Sprawdź podane tożsamości.    a) [latex]frac{1 - sin alpha }{sin alpha} cdot frac{1 + sin alpha}{cos alpha} = ctg alpha [/latex]     b) [latex]sin ^4 alpha - cos ^4 alpha = sin ^2 alpha - cos ^2 alpha [/latex]

Sprawdź podane tożsamości.    a) [latex]frac{1 - sin alpha }{sin alpha} cdot frac{1 + sin alpha}{cos alpha} = ctg alpha [/latex]     b) [latex]sin ^4 alpha - cos ^4 alpha = sin ^2 alpha - cos ^2 alpha [/latex]...

Oblicz sin alpha, tg alpha, ctg alpha, wiedząc że cos alpha = frac{2}{7}.  

Oblicz sin alpha, tg alpha, ctg alpha, wiedząc że cos alpha = frac{2}{7}.  ...

Jeżeli takie są związki: [latex]tg alpha = frac{1}{ctg alpha }\\ctg alpha = frac{1}{tg alpha } [/latex] to mogą być też takie: [latex]sin alpha = frac{1}{cos alpha }\\cos alpha = frac{1}{sin alpha } [/latex] ? Czy to nie działa w ten sposób?

Jeżeli takie są związki: [latex]tg alpha = frac{1}{ctg alpha }\\ctg alpha = frac{1}{tg alpha } [/latex] to mogą być też takie: [latex]sin alpha = frac{1}{cos alpha }\\cos alpha = frac{1}{sin alpha } [/latex] ? Czy to nie działa w ten spos...

Sprawdź tożsamość trygonometryczną: a) ( tg [latex] alpha [/latex] + ctg [latex] alpha [/latex] )^2=[latex] frac{1}{sin ^{2} alpha * cos ^{2} alpha }[/latex] b) tg[latex] alpha [/latex] - ctg [latex] alpha [/latex] = ( tg [latex] alpha [/latex] -1) (ctg

Sprawdź tożsamość trygonometryczną: a) ( tg [latex] alpha [/latex] + ctg [latex] alpha [/latex] )^2=[latex] frac{1}{sin ^{2} alpha * cos ^{2} alpha }[/latex] b) tg[latex] alpha [/latex] - ctg [latex] alpha [/latex] = ( tg [latex] alpha [/late...