if sinA+cosA=√2sin(90-A) then value of cotA
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sinA + cosA=√2sin(90-A)
or, sinA + cosA= √2cosA {as sin(90-¢)=cos¢}
or, sinA÷cosA + 1= √2 {divided by cosA}
or, tanA = (√2-1)
or, cotA= 1÷(√2-1) {as cotA= 1/ tanA}
or, cotA= (√2+1)÷{(√2+1)×(√2-1)}
or, cotA= (√2+1)÷(2-1)
or, cotA=(√2+1)
{using a^2 - b^2=(a+b)(a-b)}
or, sinA + cosA= √2cosA {as sin(90-¢)=cos¢}
or, sinA÷cosA + 1= √2 {divided by cosA}
or, tanA = (√2-1)
or, cotA= 1÷(√2-1) {as cotA= 1/ tanA}
or, cotA= (√2+1)÷{(√2+1)×(√2-1)}
or, cotA= (√2+1)÷(2-1)
or, cotA=(√2+1)
{using a^2 - b^2=(a+b)(a-b)}
rathodjagruti0pczsoh:
both
no
cot invers (√2+1) = 22.5°
good dear you did very nicely
put the value
you don't rationalise it after rationalising ans is √2+1
see the answer. I already changed it.
he had rationalize but didn't write that
yes
thnx
Answered by
6
GIVEN
sinA+cosA=√2sin(90-A)
As Sin (90 - A) = Co's A
Therefore, sinA+cosA=√2 Cos A
Sin A = √2 Cos A - Cos A
Sin A = Cos A (√2 - 1)
Sin A / Cos A = √2 - 1
As Sin A / Cos A = Tan A
Tan A = √2 - 1
TO FIND
Cot A
Therefore, Tan A = 1 / Cot A
Cot A = 1 / (√2 - 1)
Now rationalize it we get,
Cot A = [1 / (√2 - 1)] [(√2 + 1) / (√2 + 1)]
Cot A = (√2 + 1) / (2 - 1)
Cot A = (√2 + 1) / 1
Cot A = (√2 + 1)
Therefore, Cot A = √2 + 1
Tan A = √2 - 1
sinA+cosA=√2sin(90-A)
As Sin (90 - A) = Co's A
Therefore, sinA+cosA=√2 Cos A
Sin A = √2 Cos A - Cos A
Sin A = Cos A (√2 - 1)
Sin A / Cos A = √2 - 1
As Sin A / Cos A = Tan A
Tan A = √2 - 1
TO FIND
Cot A
Therefore, Tan A = 1 / Cot A
Cot A = 1 / (√2 - 1)
Now rationalize it we get,
Cot A = [1 / (√2 - 1)] [(√2 + 1) / (√2 + 1)]
Cot A = (√2 + 1) / (2 - 1)
Cot A = (√2 + 1) / 1
Cot A = (√2 + 1)
Therefore, Cot A = √2 + 1
Tan A = √2 - 1
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