Question

sin theta + cos theta is root of 2 then find cot theta

Answer 1

(sina+cosa)=√2
square both sides
sin^2a +cos^2a+2sinacosa=2
1+sin2a=2
sin2a=2-1
2a=90 degree..... (sin90=1)
a=45
cota=cot45=1
mark as brainliest if helped... lol

Answer 2

Hi ,

Here I am using A instead of theta ,

**************************

1 ) sin² A + cos² A = 1

2 ) 2sinAcosA = sin 2A

3 ) sin 90° = 1

****************************

sin A + cosA = √2 -----( 1 )

Squareing equation ( 1 ) , we get

( sinA + cosA )² = ( √2 )²

sin² A + cos² A + 2sinAcosA = 2

1 + 2sinAcosA = 2

2sinAcosA = 2 - 1

Sin2A = 1

Sin 2A = sin 90°

2A = 90°

A = 90/2

A = 45°

Therefore ,

Cot A = cot 45°

= 1

I hope this helps you.

:)