If tan{\alpha}+cot{\alpha}=2, then {tan{\ }}^{20}\alpha+{cot{\ }}^{20}\alpha is equ

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Solution

Q.
If $I f t a n α + c o t α = 2, t h e n {t a n}^{20} α + {c o t}^{20} α i s e q u a l t o$

1 0

2 2

3 20

4 $2^{20}$

Ans.
(2)

We have,

$t a n α + c o t α = 2 \Rightarrow t a n α + \frac{1}{\tan α} = 2 \Rightarrow {t a n}^{2} α - 2 t a n α + 1 = 0 \Rightarrow (t a n α - 1)^{2} = 0 \Rightarrow t a n α = 1 \Rightarrow α = 45 ° S o, t a n α = c o t α = 1 N o w, {t a n}^{20} α + {c o t}^{20} α = 1^{20} + 1^{20} = 1 + 1 = 2$

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