已知tan α=2,求2/3 (sin² α)+1/4(cos² α)的值

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已知tanα=2,求2/3(sin²α)+1/4(cos²α)的值已知tanα=2,求2/3(sin²α)+1/4(cos²α)的值已知tanα=2,求2/3(

已知tan α=2,求2/3 (sin² α)+1/4(cos² α)的值
已知tan α=2,求2/3 (sin² α)+1/4(cos² α)的值

已知tan α=2,求2/3 (sin² α)+1/4(cos² α)的值
tanα=sinα/cosα=2
sin²α/cos²α=4
又sin²α+cos²α=1
∴sin²α=4/5 cos²α=1/5
(2/3)sin² α+(1/4)cos² α
=(2/3)*(4/5)+(1/4)(1/5)
=(32+3)/60
=7/12

2/3 (sin² α)+1/4(cos² α)
=[2/3 (sin² α)+1/4(cos² α)]/1
=[2/3 (sin² α)+1/4(cos² α)]/(sin² α+cos² α) 分子分母同时除以cos² α
=[2/3*tan^2a+1/4]/(tan^2a+...

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2/3 (sin² α)+1/4(cos² α)
=[2/3 (sin² α)+1/4(cos² α)]/1
=[2/3 (sin² α)+1/4(cos² α)]/(sin² α+cos² α) 分子分母同时除以cos² α
=[2/3*tan^2a+1/4]/(tan^2a+1) tan α=2
=[8/3+1/4]/(4+1)
=7/144

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∵tan α=2 ∴cota=1/2
∴2/3 (sin² α)+1/4(cos² α)=2/3 csc²a+1/4 sec²a
=2/3 (1+cot²a)+1/4(1+tan²a)
=2/3×(1+1/4)+1/4×(1+4)
=5/6+5/4
=25/12