Question

If sin θ + cos θ = √2 cos(90° - θ ) , find cot θ?

Answer 1

Hey there! Thanks for the question.

sin θ + cos θ = √2 cos(90° - θ ) 

sin θ + cos θ = √2 sin θ

cos θ = √2 sin θ- sin θ

cos θ= (√2-1) sin θ

cos θ/ sin θ= (√2-1) 

cot θ= (√2-1).

Answer 2

Hi !

Actually there are more than 1 method , to solve this question , I'm using the simpler one ,

Given,
sin θ + cos θ = √2 cos(90° - θ )

But , we know that ,

cos(90° - θ ) = sin θ ( complementary angles)

So,
sin θ + cos θ = √2 sin θ

Taking sin θ to RHS,
cos θ = √2 sin θ- sin θ

Taking sin θ common ,
cos θ = sin θ(√2-1)

cos θ/ sin θ= (√2-1)

But , we know that :-
cos θ/ sin θ = cot θ


Hence,
cot θ= (√2-1).