sinA + cosA = √2. Evaluate tanA + cotA
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Answered by
3
Given Sin A + cos A = root 2
On squaring both sides, we get
(sinA + cosA)^2 = (root)^2
We know that (a + b)^2 = a^2 + b^2 + 2ab
sin^2A + cos^2A + 2sinAcosA = 2
1 + 2sinAcosA = 2
2sinAcosA = 1
We know that 2sinAcosA = sin2A
sin2A = sin90
2A = 90
A = 45.
Now,
Tan A + cotA = Tan(45) + cot(45)
= 1 + 1
= 2.
Hope this helps!
On squaring both sides, we get
(sinA + cosA)^2 = (root)^2
We know that (a + b)^2 = a^2 + b^2 + 2ab
sin^2A + cos^2A + 2sinAcosA = 2
1 + 2sinAcosA = 2
2sinAcosA = 1
We know that 2sinAcosA = sin2A
sin2A = sin90
2A = 90
A = 45.
Now,
Tan A + cotA = Tan(45) + cot(45)
= 1 + 1
= 2.
Hope this helps!
Rahi39:
After 2sinAcosA = 1, I didn't understand how to convert it
nice
bro
2sinAcosA= sin2A
sin2A = 1
sin2A = sin90
2A = 90
A = 45
sin2A = 1
sin2A = sin90
2A = 90
A = 45
2 SinA cosA = sin2A is the formula. Next step is sin90 = 1
oh....got it
Thank you
Answered by
3
sinA+cosA =√2
squaring both sides we get
2sinAcosA =1. sinACosA=1/2
then tanA +cotA = sinA/cosA +cosA/sinA
=sin^2A +cos^2A)/sinA×cosA
=1/(1/2)
=2
squaring both sides we get
2sinAcosA =1. sinACosA=1/2
then tanA +cotA = sinA/cosA +cosA/sinA
=sin^2A +cos^2A)/sinA×cosA
=1/(1/2)
=2
I didn't understand the 3rd step. 2 sinAcosA = 1
On squaring both sides, The right side value will be 2 not 1.I think
(sinA+cosA)^2=(√2)^2 .sin^2A+cos^2A+2sinAcosA =2. then 1+2SinAcosA..=2. then2sinAcosA=2-1. then2sinAciosA=1
now this helps you.
Now I have understood. Kindly try to explain step by step.
next time,i will write all steps. [OM SAI RAM*,]
Thank you so much
Thank You
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