tanα=2,求3sin²α-sinαcosα+1的值.

tanα=2,求3sin²α-sinαcosα+1的值.
tanα=2,求3sin²α-sinαcosα+1的值.

tanα=2,求3sin²α-sinαcosα+1的值.
3sin²a-sinacoa+1
=3sin²a-sinacosa+sin²a+cos²a
=4sin²a+cos²a-sinacosa
=(4sin²a+cos²a-sinacosa)/(sin²a+cos²a)
=(4tan²a+1-tana)/(tan²a+1)
=(4×2²+1-2)/(2²+1)
=15/5
=3

3sin²α-sinαcosα+1
=3(1-cos2α)/2-1/2sin2α+1
=3/2-3/2*cos2α-1/2sin2α+1
=-3/2*cos2α-1/2sin2α+5/2
=-3/2*(1-tan²α)/(1+tan²α)-1/2*2tan²α/(1+tan²α)+5/2
=-3/2*(1-2...

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3sin²α-sinαcosα+1
=3(1-cos2α)/2-1/2sin2α+1
=3/2-3/2*cos2α-1/2sin2α+1
=-3/2*cos2α-1/2sin2α+5/2
=-3/2*(1-tan²α)/(1+tan²α)-1/2*2tan²α/(1+tan²α)+5/2
=-3/2*(1-2²)/(1+2²)-tanα/(1+tan²α)+5/2
=-3/2*(1-2²)/(1+2²)-2/(1+2²)+5/2
=-3/2*(-3)/5-2/5+5/2
=9/10-4/10+5/2
=1/2+5/2
=3

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