Question

If sin θ − cos θ = 0 and 0°<θ<90 find theta

Answer 1

↑ Here is your answer ↓
_____________________________________________________________
_____________________________________________________________

Given:

$sin \theta - cos \theta = 0$

$sin \theta = cos \theta$

The only possibility is,

$sin45^o = cos45^o$

$1=1$

Or,

$\frac{sin \theta}{cos \theta} = 1$

$tan \theta = 1$

$\theta = 45^o$

Answer 2

Heya user ,
Here is your answer !!

Given ,

sin θ − cos θ = 0
=> sin θ = cos θ
=> tan θ = 1
=> tan θ = tan 45 degree
=> θ = 45 degree .... [ Ans ]


# ALTERNATIVE PROCESS #

Given ,

sin θ − cos θ = 0 .... ( i )
=> ( sin θ − cos θ )^2 = 0
=> sin^2 θ - 2sin θ cos θ + cos^2 θ = 0
=> 1 = 2sin θ cos θ .

Now ,
( sin θ + cos θ )^2
= sin^2 θ + cos^2 θ + 2 sin θ cos θ
= 1 + 1
= 2 .

Therefore , sin θ + cos θ = √2 ... ( ii )

Solving ( i ) and ( ii ) , we get ,
sin θ + cos θ = √2
sin θ − cos θ = 0

=> 2 sin θ = √2
=> sin θ = √2 / 2
=> sin θ = 1 / √2
=> sin θ = sin 45 degree
=> θ = 45 degree ....... [ Ans ]

Hope it helps you !!