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if sin x + cos x=√2 cos (90-x), then cot x is equal to

if sin x + cos x=√2 cos (90-x), then cot x is equal to

Grade:12th pass

3 Answers

Arun
25750 Points
6 years ago
Dear Gaurav
 
sinθ+cosθ=√2cos(90- θ)
= sinθ + cosθ = √2sinθ
= (sinθ + cosθ)/sinθ = √2sinθ/sinθ                     [dividing both sides by sinθ ]
=  1 + cotθ  = √2
=  cotθ = √2-1
 
 
Regards
Arun (askIITians Forum expert)
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the attached solution to your problem below.
 
sinx + cosx = √2cos(90- x)
= sinx + cosx = √2sinx
= (sinx + cosx)/sinx = √2sinx/sinx                     [dividing both sides by sinx ]
=  1 + cotx  = √2
=  cotx = √2-1
 
Thanks and regards,
Kushagra
Arjun Raj
15 Points
3 years ago
sinx + cosx = √2 cos(90-x)
sinx + cos x=√2 sinx
(sinx + cosx)/sinx =√2
sinx/sinx + cosx/cosx =√2
1+ cotx =√2
cotx = √2 -1

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