Question

计算tan(15°-α)tan(380°+α)tan(75°+α)tan(290°+α)=

Answer 1

根据诱导公式,得

tan(15°-α)tan(380°+α)tan(75°+α)tan(290°+α)

=tan(15°-α)tan(20°+α)tan(75°+α)cot(20°+α)

=tan(15°-α)tan(20°+α)cot(15°-α)cot(20°+α)

=tan(15°-α)cot(15°-α)tan(20°+α)cot(20°+α)

=1x1

=1

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