cosx+secx=2 ...(i) On squaring both sides, we get cos2x+sec2x+2=4 ⇒ cos2x+sec2x=2 ...(ii) On cubing equation (i), we get cos3x+sec3x+3(cosx+secx)=8 ⇒ cos3x+sec3x+(3×2)=8 ⇒ cos3x+sec3x=2 ...(iii) Similarly, when we multiply n in power both sides,cosnx+secnx=2 Alternate Method: If we put x=0° then cos0°+sec0°=1+1=2 Similary cosecnx+secnx =cosecn0°+secn0° =1+1=2