Question

If tanA + cotA = 5 , then find the value of tan^2A + cot^2A

Answer 1

tanA + cotA = 5

(tanA +cotA)2 = tanA2 + cotA2 + 2(tanA * cotA)
25 = tanA2 + cot2A + 2
tanA *cotA = 1

tan2A + cot2A = 23

Answer 2

Answer:

$The \: value \: of \\\: tan^{2}A+cot^{2}A+2 = 23$

Step-by-step explanation:

$Given \: tanA+cotA = 5--(1)$

On Squaring both sides of the equation (1) , we get

$(tanA+cotA)^{2}=5^{2}$

$\implies tan^{2}A+cot^{2}A\\+2tanAcotA = 25$

/* We know that,

$1) (a+b)^{2} = a^{2}+b^{2}+2ab$

$2) tanAcotA =1$*/

$\implies tan^{2}A+cot^{2}A+2 = 25$

$\implies tan^{2}A+cot^{2}A= 25-2$

$\implies tan^{2}A+cot^{2}A = 23$

Therefore,

$The \: value \: of\\ \: tan^{2}A+cot^{2}A+2 = 23$

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