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IfcosA+sinA =√2cosA,prove that cosA-sinA=√2sinA
Asked by Soumyaputtige262 | 01 Oct, 2018, 08:55: PM
cosA + sinA = √2 cos A
(cosA + sinA)2 = 2cos2 A
cos2 A + 2sinA cosA + sin2 A =  2cos2 A
1 - sin2 A + 2sinAcosA + 1 - cos2 A = 2cos2 A
2 - 2cos2 A = cos2 A + sin2 A - 2sinAcosA
2(1 - cos2 A) = (cosA - sinA)2
2sin2A = (cosA - sinA)2
cosA - sinA = √2 sinA
AA
CosA +sinA = √2cosA
squaring
⇒(cosA + sin A)² = (√2cosA)²
⇒cos²A + sin²A + 2sinAcosA = 2cos²A
⇒1 - sin²A + 1 - cos²A + 2sinAcosA = 2cos²A
⇒2 - 2cos²A = cos²A + sin²A - 2sinAcosA
⇒2(1 - cos²A)= (cosA - sinA)²
⇒ cosA - sinA = √[2sin²A]
⇒cosA-sinA = √2sinA

Answered by Sneha shidid | 03 Oct, 2018, 10:19: AM

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