Question

cos0+sin0=(2)^1/2 cos0 then prove that cos0-sin0=(2)^1/2sin0​

Answer 1

Step-by-step explanation:

we have to prove ,cosΦ -sinΦ =(2)½ sinΦ , we have given cosΦ+sinΦ=(2)½cosΦ

Therefore ,

cosΦ + sinΦ = (2)½ cosΦ= √2 cosΦ

sinΦ = √2 cosΦ - cosΦ

sinΦ = cosΦ (√2 - 1)

sinΦ /(√2-1)=cosΦ

cosΦ ={sinΦ /(√2-1)}{(√2+1)/(√2+1)}

cosΦ = {√2 sinΦ + sinΦ}/{2-1}

cosΦ - sinΦ = √2sinΦ

Hence proved