Give the solution of Qno. 3 Qno.5 Qno. 10

​Q3. Find the distance between the points (a cos 45°, 0) and (0 , a cos 45°)

​Q5. A number X is chosen from the numbers –5, –4, –3, –2, –1, 0 , 1, 2, 3, 4, 5. What is the provability that 1  x 1 < 4?

Q10. If Cos A – sin A = 1, prove that Cos A + sin A =  ± 1.
 

cosA-sinA=1Squaring both sides, we getcosA-sinA2=1cos2A+sin2A-2sinA cosA=1    a-b2=a2+b2-2ab1-2sinA cosA=1    sin2x+cos2x=1sinAcosA=0   ..(1)Consider,sinA+cosA2=sin2A+cos2A+2sinAcosA   a+b2=a2+b2+2ab=1+2(0)     [using 1]=1So, sinA+cosA2=1sinA+cosA=±1
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