Question

If cosQ+sinQ=√2then cosQ=?

Answer 1

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Answer 2

cosQ+sinQ=√2

square both sides

(cosQ + sinQ)²=(√2)²

cos²Q + sin²Q+2cosQsinQ=2

1+2cosQsinQ=2

2cosQsinQ=2-1

2cosQsinQ=1

cosQsinQ=1/2 {sin2A=2sinAcosA}

sin2Q/2=1/2

sin2Q=1

sin2Q=sin90

2Q=90

Q=90/2

Q=45°

•°• cosQ=cos45=1/√2

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