Question

if tan^3 theta + cot^3=52 then find tan^2theta+cot^2theta=?

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

Hi your answer is as follows,

Step-by-step explanation:

$we~can~write~it~in~the~form~of~(a+b)^3-3ab(a+b)=a^3+b^3\\therefore,\\(tan+cot)^3-3tan*cot(tan+cot)=52\\(tan+cot)^3-3(tan+cot)\\Taking~tan+cot~as ~common~we~get,\\(tan+cot)[(tan+cot)^2-3]=52\\Let~tan+cot=x\\x(x^2-3)=52\\x^3-3x=52\\using~trial~and~error~method~we~get,\\x=4\\=>~tan+cot=4\\squaring~both~sides~we~get,\\tan^2+cot^2+2tan*cot=16\\=tan^2+cot^2+2=16\\=tan^2+cot^2=14$

Therefore value of $tan^2+cot^2$ = 14

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