Question

已知tanα+inα=a，tanα-sinα=b，求证（a²-b²)²=16ab

Answer 1

(a^2-b^2)^2
=(a+b)^2(a-b)^2
=(tanα +sinα +tanα -sinα)^2(tanα +sinα -tanα +sinα)^2
=(2tanα)^2(2sinα)^2
=16tan^2αsin^2α

16ab=16*( tanα +sinα )(tanα -sinα)
=16(tan^2α -sin^2α )
=16(sin^2α/cos^2α-sin^2α)
=16( sin^2α-sin^2αcos^2α)/cos^2α
=16(sin^2α(1-cos^2α)/塌镇厅团隐旅颂cos^2α
=16sin^2asin^2a/cos^2α
=16tan^2αsin^2α

(a^2-b^2)^2=16ab

Answer 2

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