If tan A+ cot A = 4, find the value of tan*A + cot4A
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Answer:
> tan^4A + cot^4A = 194.
Step-by-step explanation:
tanA+cotA=4
(squaring both sides)
(tanA+cotA)
2
=4
2
⇒tan
2
A+cot
2
A+2(tanA)(cotA)=16
⇒tan
2
A+cot
2
A+2=16
⇒tan
2
A+cot
2
A=16−2
⇒tan
2
A+cot
2
A=14
(on squaring both sides)
⇒(tan
2
A−cot
2
A)
2
=(14)
2
tan
4
A+cot
4
A+2(tan
2
A)(cot
2
A)=196
tan
2
A+cot
4
A=196−2
=194
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