Question

If tan α + cot α = 2, then tan⁸α + cot⁸α = ​

Answer 1

Answer:

2is the answer

Step-by-step explanation:

the answer is 2

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ \tan \alpha + \cot \alpha = 2}$

TO DETERMINE

$\displaystyle \sf{ {\tan}^{8} \alpha + {\cot}^{8} \alpha }$

EVALUATION

Here it is given that

$\displaystyle \sf{ \tan \alpha + \cot \alpha = 2}$

$\displaystyle \sf{ \implies \: \tan \alpha + \frac{1}{\tan \alpha } = 2}$

$\displaystyle \sf{ \implies \: \frac{{\tan}^{2} \alpha + 1}{\tan \alpha } = 2}$

$\displaystyle \sf{ \implies \: {\tan}^{2} \alpha + 1 = 2\tan \alpha }$

$\displaystyle \sf{ \implies \: {\tan}^{2} \alpha + 1 - 2\tan \alpha = 0}$

$\displaystyle \sf{ \implies \: {(\tan \alpha - 1)}^{2} = 0}$

$\displaystyle \sf{ \implies \: (\tan \alpha - 1) = 0}$

$\displaystyle \sf{ \implies \: \tan \alpha = 1}$

$\displaystyle \sf{ \implies \cot \alpha = 1}$

This gives

$\displaystyle \sf{ {\tan}^{8} \alpha + {\cot}^{8} \alpha }$

$\displaystyle \sf{ = {1}^{8} + {1}^{8} }$

$\sf{ =1 + 1}$

$= 2$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If cosθ+secθ=√2,find the value of cos²θ+sec²θ

https://brainly.in/question/25478419

2. Value of 3 + cot 80 cot 20/cot80+cot20 is equal to

https://brainly.in/question/17024513

3. In a triangle, prove that (b+c-a)(cotB/2+cotC/2)=2a×cotA/2

https://brainly.in/question/19793971