Question

If cos A + Sin A =√2 Cos A , Prove that cos A - Sin A = √2 Sin A
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Answer 1

cos A+sin A=$\sqrt{2}$ cos A

To prove: cos A-sin A=$\sqrt{2}$ sin A

ANSWER: cos A+sin A=$\sqrt{2}$ cos A      

                 squaring both sides

                 $(cos A+ sin A)^{2}$ =$( \sqrt{2} cos A)^{2}$

                 $cos^{2} A$+$sin^{2} A$ + 2 cos A. sin A = 2$cos^{2} A$

                2 cos A. sin A=2 $cos^{2} A$-($cos^{2} A$+ $sin^{2} A$)

                2 cos A. sin A=$cos^{2} A$ - $sin^{2} A$

                2 cos A. sin A= (cos A+sin A)(cos A- sin A)

                2 cos A. sin A= ($\sqrt{2}$ cos A)(cos A- sin A)

                (cos A- sin A)=2 cos A. sin A/$\sqrt{2}$ cos A

                cos A- sin A=√2 Sin A

                      hence proved

hope it helped u its an easy method to prove

remember not to put value of $cos^{2} A$+$sin^{2} A$=1 in second step its an important step....

have a nice day..keep practicing and ask questions:):):):):):):):)