The numerical value of tan 20 tan 80 cot 50 =
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Step-by-step explanation:
tan20tan80cot50
=
tan(60−10)
tan(30−10)tan(90−10)
=
1+tan60tan10
tan60−tan10
1+tan30tan10
tan30−tan10
cot10
=
tan10
1+
3
tan10
3
−tan10
1+
3
1
tan10
3
1
−tan10
=
tan10⋅
1+
3
tan10
3
−tan10
3
+tan10
1−
3
tan10
=
tan10(3−tan
2
10)
1−3tan
2
10
=
3tan10−tan
3
10
1−3tan
2
10
=
tan3(10)
1
=
tan30
1
=
3
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