Math, asked by luharapini, 4 months ago

If cos − sin = √2 sin , show that cos + sin = √2 cos .

Answers

Answered by noorjahanliakath
1

Answer:

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Answered by hussainpk5242
1

Answer:

Step-by-step explanation:

we want to show that cos+sin=√2cos

given

cos − sin = √2 sin // squaring on both side and we get

  • cos²+sin²-2cossin=2sin²
  • cos²=2sin²-sin²+2cossin // adding cos² on boht side
  • cos²+cos²=sin²+cos²+2sincos // (a²+b²+2ab)=a²+b² so
  • 2cos²=(sin+cos)² // square root on both side and we get
  • √2cos=sin+cos // so prove
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