已知tanα=2,求sin²α+sinαcosα-2cos²α=?
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已知tanα=2,求sin²α+sinαcosα-2cos²α=?
已知tanα=2,求sin²α+sinαcosα-2cos²α=?
已知tanα=2,求sin²α+sinαcosα-2cos²α=?
tanα=2
sinα/cosα=2
sinα=2cosα
sin²α+sinαcosα-2cos²α
=(sinα+2cosα)(sinα-cosα)
=(2cosα+2cosα)(2cosα-cosα)
=4(cosα)^2
=4*(1+cos2α)/2
=2+2cos2α
=2+2[1-(tanα)^2]/[1+(tanα)^2]
=2+2[1-2^2]/[1+2^2]
=2-6/5
=4/5
因为 tan α=2,
所以 原式= [ (sin α)^2 +sin α cos α -2 (cos α)^2 ] / [ (sin α)^2 +(cos α)^2 ]
= [ (tan α)^2 +tan α -2 ] / [ (tan α)^2 +1 ] ...
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因为 tan α=2,
所以 原式= [ (sin α)^2 +sin α cos α -2 (cos α)^2 ] / [ (sin α)^2 +(cos α)^2 ]
= [ (tan α)^2 +tan α -2 ] / [ (tan α)^2 +1 ]
= (2^2 +2 -2) /(2^2 +1)
= 4/5.
= = = = = = = = =
弦化切.
即 先除以 (sin α)^2 +(cos α)^2, 然后分子分母同时除以 (cos α)^2.
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