Question

If sin theta plus cos theta is 1 then what is value of sin theta minus cos theta

Answer 1

❏ Question

If sin θ + cos θ = 1 then what is value of sin θ - cos θ = ?

❏ Solution

Given:-

• sin θ + cos θ = 1 .............(1)

Find :-

• sin θ - cos θ = ?

❏ Explanation

we know,

★ sin² θ + cos² θ = 1 ............(2)

So, now

Squaring both side of equ(1),

➩ ( sin θ + cos θ )² = 1²

➩ sin² θ + cos² θ + 2.sin θ. cos θ = 1

keep value by equ(2),

➩ 1 + 2.sin θ. cos θ = 1

➩ 2.sin θ. cos θ = 1 - 1

➩ 2.sin θ. cos θ = 0

➩ sin θ. cos θ = 0 ................(3)

We have,

★ sin θ - cos θ = √[(sin θ + cos θ)² - 4.sin θ cos θ ]

Keep value by equ(1) and equ(3)

➩ sin θ - cos θ = √[(1)² - 4.0]

➩ sin θ - cos θ = √(1-0)

➩ sin θ - cos θ = √1

➩ sin θ - cos θ = 1 [Ans]