Question

If sin x +cos x =√2 sin(90 - x) then find the value of cot x .​

Answer 1

Answer: NOTE I HAVE TAKEN X AS A.

Step-by-step explanation:

Given  

sinA+cosA=  

2

​  

sin(90−A)

⇒  

2

​  

 

1

​  

sinA+  

2

​  

 

1

​  

cosA=sin(90−A)

⇒sinA.cos45  

∘

+cosA+sin45  

∘

=sin(90−A)

⇒(A+45  

∘

)=sin(90  

∘

−A)  

Equating  

A+45=90−A

⇒2A=45  

∘

 

⇒A=22  

2

1

​  

 

∘

 

A=  

8

π

​  

 

∴cotA=cot  

8

π

​  

=  

2

​  

+1

Answer 2

Answer:

Step-by-step explanation:

Given  

sin A +cos A =√2sin(90−A)

⇒1/√2 sin A+1/√2 sin A=sin(90°-A)

$sinA.cos45 +cosA+sin45 =sin(90-A)$

$(A+45 )=sin(90 -A) \\Equating A+45=90-A2A=45 '$

⇒A=22 1/2.

$A=\pi /8\\\\cot A=cot\pi /8=$

√2+1.

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