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CosA+SinA=√2CosA then prove that CosA-SinA=√2SinA

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CosA+SinA=√2CosA then prove that CosA-SinA=√2SinA

Posted by Yogesh Kumar 6 years, 7 months ago

CBSE > Class 10 > Mathematics

2 answers

Paulo Dybala 6 years, 7 months ago

From given eqn 1 SinA = √2 cosA - cos A SinA = cosA(√2 - 1) SinA /√2-1 = cosA Rationalising SinA × √2 + 1 ----------------------- = cosA √2 - 1 × √2 +1 √2 sinA + sinA. = CosA ------------------------- 2 - 1 √ 2 sinA =. CosA - SinA Hence proved?

2Thank You

Nishihoney Lodha 6 years, 7 months ago

By squaring both sides: (cosA+sinA)2=(√2cosA)2 By adding (cosA +sinA)2 +( cosA -sinA)2----------->cos2A+sin2A+2cosAsinA+cos2A+sin2A-2cosAsinA---------->cos2A+sin2A+cos2A+sin2A------>1+1=2. Now,(cosA-sinA)2=2-(cosA+sinA)2-------->so, (cosA-sinA)2=2-2cos2A------>(cosA-sinA)2=2(1-cos2A)------>(cosA-sinA)2=2sin2A-------->(cosA-sinA)=√2sinA.... Hence,proved. (Here 2 is the power.)

1Thank You

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