Saved Bookmarks
| 1. |
CosA+SinA=√2CosAthen prove thatCosA-SinA=√2SinA |
|
Answer» From given eqn 1SinA = √2 cosA - cos A SinA = cosA(√2 - 1)SinA /√2-1 = cosARationalising SinA × √2 + 1----------------------- = cosA√2 - 1 × √2 +1√2 sinA + sinA. = CosA------------------------- 2 - 1 √ 2 sinA =. CosA - SinA Hence proved? By squaring both sides: (cosA+sinA)2=(√2cosA)2By 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.) |
|