Question

If Cos o + sin o = √2
Prove that Cos 0 - sino = √2 sin o ​

Answer 1

Answer:

Step-by-step explanation:

i will be using A instead of o

we have ,

cosA - sinA=√2 sinA

squaring both the sides

=>(cosA - sinA)²=2 sin²A

=>cos²A+sin²A-2sinAcosA=2sin²A

=>sin²A-2sin²A-2sinAcosA= -cos²A

=> -sin²A-2sinAcosA= -cos²A

=> sin²A+2sinAcosA=cos²A

adding cos²A on both the sides

=> cos²A+sin²A+2sinAcosA=2cos²A

=> (cosA+sinA)²=2cos²A

=> cosA+sinA=√2cosA

Answer 2

Answer:

Step-by-step explanation:

cos0 + sin0 = $\sqrt{2}$                         (given)

$(cos0 + sin0)^{2}$= 2                          (squaring both sides)

$cos^{2}0$  + $sin^{2}0$ + 2cos0.sin0 = 2   ( $cos^{2}0$  + $sin^{2}0$ = 1)

1 + 2cos0.sin0 = 2

2cos0.sin0=2 - 1

cos0.sin0 = 1÷2      

sin0 = 1/2cos0-------------{1}

                       

Else, you can solve.