If \cos \theta+\sin \theta=\sqrt{2} \cos \theta, Prove that\cos \theta

1.	If \cos \theta+\sin \theta=\sqrt{2} \cos \theta, Prove that\cos \theta-\sin \theta=\sqrt{2} \sin \theta
Answer» cosA +sinA= √2cosA => sinA= √2cosA- cosA => sinA = cosA(√2 -1) Now multiplying both side by ( √2+1) =>sinA(√2+1) = cosA(√2–1)(√2+1) =>√2sinA + sinA=cosA(2–1) => cosA-sinA= √2sinA (Answer)

If \cos \theta+\sin \theta=\sqrt{2} \cos \theta, Prove that\cos \theta-\sin \theta=\sqrt{2} \sin \theta

Answer»

cosA +sinA= √2cosA

=> sinA= √2cosA- cosA

=> sinA = cosA(√2 -1)

Now multiplying both side by ( √2+1)

=>sinA(√2+1) = cosA(√2–1)(√2+1)

=>√2sinA + sinA=cosA(2–1)

=> cosA-sinA= √2sinA (Answer)