Question

if sinA +cosA =√2, Then evAluate :tanA+cotA

Answer 1

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Answer 2

Answer:

$tanA+cotA =2$

Step-by-step explanation:

Given :SinA +cosA =√2

To Find : tanA+cotA

Solution :

$SinA +cosA =\sqrt{2}$

Squaring both sides

$(SinA +cosA)^2 =(\sqrt{2})^2$

$Sin^2A +Cos^2A+2sina A cosA =2$

Identity : $Sin^2A+cos^2A = 1$

$1+2sin A cosA =2$

Identity : $2 sinx cos x= sin2x$

$Sin2A =1$

$Sin2A =Sin90$

So, 2A= 90m

A= 45

So, $tanA+cotA = Tan 45+Cot 45 = 1+1=2$

Hence  $tanA+cotA =2$