Question

If tanø+cotø=2, show that tan⁷ø+cot⁷ø=2​

Answer 1

Step-by-step explanation:

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Answer 2

Hi there !!

Ø = A ( I am taking A instead of thetha)

It is given that, tanA+ CotA= 2

TanA + 1/tanA = 2 {We now that cotA =1/tanA)

Now, tan²A+ 1=2tanA

Tan²A-2tanA+1=0

(Let tanA be x so it will become quadratic equation)

TanA + 1/tanA = 2

{We now that cotA =1/tanA)

Now,

tan²A+ 1=2tanA

Tan²A-2tanA+1=0(Let tanA be x so it will become quadratic equation)

x²-2x+1=0

x²-x-x+1=0

x(x-1) -1(x-1)

(x-1)²=0 or x=1

Means, tanA =1 Value of tan^7+cot^7

(1)^7+(1/1)^7= 2

Thankyou :)