14. (98-1-54) Укажите значение дроби.
[tex] \frac{2 \cos ^{2} ( { \alpha } ) - \sin(2 \alpha ) }{2 \sin ^{2} ( \alpha ) - \sin(2 \alpha ) } [/tex]
[tex] \frac{2 \cos ^{2} ( { \alpha } ) - \sin(2 \alpha ) }{2 \sin ^{2} ( \alpha ) - \sin(2 \alpha ) } [/tex]
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Ответ:
4
Объяснение:
ctg(a)=1/tg(a)= -4
sin(2a)=2sin(a)*cos(a)
(cos(a)-sin(a))/(sin(a)-cos(a))= -1
(2cos²(a)-2sin(a)*cos(a))/(2sin²(a)-2sin(a)*cos(a))
(2cos(a)*(cos(a)-sin(a)))/(2sin(a)*(sin(a)-cos(a)))
(cos(a)*(cos(a)-sin(a)))/(sin(a)*(sin(a)-cos(a)))
ctg(a)*(cos(a)-sin(a))/(sin(a)-cos(a))
-4(cos(a)-sin(a))/(sin(a)-cos(a))
-4*(-1)=4