Question

if tanA + cotB = 2 then find the value of tan²A + cot²B​

Answer 1

Answer:

1

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Answer 2

Step-by-step explanation:

$Given: It is given that tanA+cotA=2tanA+cotA=2$

$To find: The \;value \;of\; tan^2A+cot^2Atan </p><p>2 A+cot 2 A$

$Solution:$

$It\; is \;given \;that\; tanA+cotA=2tanA+cotA=2 , then$

$Squaring\; on \;both \;the sides, \;we\; have$

$(tanA+cotA)^2=4(tanA+cotA) 2 =4$

$tan^2A+cot^2A+2tanAcotA=4tan 2 A+cot 2 A+2tanAcotA=4$

$Now,\; because\; tanAcotA=1tanAcotA=1 , therefore \;the\; equation \;becomes,$

$➵tan^2A+cot^2A+2=4tan 2 A+cot 2 A+2=4$

$➵tan^2A+cot^2A=2tan 2 A+cot 2 A=2$

$➵Thus \;, the \;value\; of\; tan^2A+cot^2Atan cot2 A+cot 2 A will be 2$