Question

If cos 0 + sin 0 = root2 cos0 prove that
cos0 - sin 0 = root2 sin0​

Answer 1

Answer:

cos0+sin0=root2 cos0

sin0=cos0(root2 -1

)

Answer 2

Step-by-step explanation:

Given:-

cos 0 + sin 0 = root2 cos0

To find:-

If cos 0 + sin 0 = root2 cos0 prove that

cos0 - sin 0 = root2 ssin0

Solution:-

Given that:

LHS:-

Cos 0 + Sin 0 = √2 Cos 0

=>Sin 0 = √2 Cos 0 - Cos 0

=>Sin 0 = (√2-1) Cos 0

=>Sin 0/ Cos 0 = √2-1

On Rationalising the √2-1

=>Sin 0/ Cos 0 = (√2-1)(√2+1)/(√2+1)

=> Sin 0 / Cos 0 = (2-1)/(√2+1)

since (a+b)(a-b)=a^2-b^2

=> Sin 0/ Cos 0 = 1/(√2+1)

On applying cross multiplication then

=>(√2+1) Sin 0 = 1×Cos 0

=>√2 Sin 0 + Sin 0 = Cos 0

=>√2 Sin 0 = Cos 0 - Sin 0

Therefore, Cos 0 - Sin 0 = √2 Sin 0

= RHS

LHS= RHS

Answer:-

If cos 0 + sin 0 = √2 cos 0 then cos0- sin 0 = √2 sin 0