Question

cosA+sinA=√2cosA then prove that cosA-sinA =✓2sinA​

Answer 1

cos A + sin A=√2cos A
or, (cos A+sin A)/cos A= √2
or, (cosA/cosA)+(sinA/cosA)= √2
or, 1+tan A= √2
or, tan A= √2−1

cos A - sin A=√2sin A
or, (cos A-sin A)/sin A= √2
or, (cosA/sinA)-(sinA/sinA)= √2
or, cot A-1 =√2
or, cot A= √2+1

Therefore multiplying both,
cotA.tanA=((√2+1)(√2−1))
1=(√2)²-1= 2-1=1

Answer 2

Answer:

please refer to the attachment

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