If theta in an acute angle and tan theta+cot theta=2.then find the value of tan^7 theta+cot^7theta =?
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Howdy!!
your answer is --
Given,
tan∅ + cot∅ = 2
=> tan∅ + 1/tan∅ = 2
=> tan^2∅ + 1 = 2tan∅
=> tan^2∅ - 2tan∅ + 1 = 0
now,factories it
=> tan^2∅ - tan∅ - tan∅ + 1 = 0
=> tan∅ ( tan∅ - 1 ) -(tan∅-1) = 0
=> (tan∅ - 1) (tan∅-1) = 0
=> tan ∅ = 1
=> tan∅ = tan45° [ since tan45° = 1 ]
=> ∅ = 45°
now , tan^7∅ + cot^7∅
= tan^7 45° + cot^7 45°
= 1 + 1
= 2
==============================
hope it help you
your answer is --
Given,
tan∅ + cot∅ = 2
=> tan∅ + 1/tan∅ = 2
=> tan^2∅ + 1 = 2tan∅
=> tan^2∅ - 2tan∅ + 1 = 0
now,factories it
=> tan^2∅ - tan∅ - tan∅ + 1 = 0
=> tan∅ ( tan∅ - 1 ) -(tan∅-1) = 0
=> (tan∅ - 1) (tan∅-1) = 0
=> tan ∅ = 1
=> tan∅ = tan45° [ since tan45° = 1 ]
=> ∅ = 45°
now , tan^7∅ + cot^7∅
= tan^7 45° + cot^7 45°
= 1 + 1
= 2
==============================
hope it help you
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