Given: π / 2 < x < π i.e x lies in the 2nd quadrant where all trigonometric ratios are negative except sin and cosec. ⇒√2+√2+2cos2x=√2+√2(1+cos2x) As we know that, cos2x=2cos2x–1 or 1+cos2x=2cos2x ⇒√2+√2+2cos2x=√2+√2×2cos2x ⇒√2+√2+2cos2x=√2±2cosx As x lies in 2nd quadrant ⇒√2+√2+2cos2x=√2−2cosx ⇒√2+√2+2cos2x=√2(1−cosx) As we know that, cosx=1−2sin2(x∕2) or 2sin2(x∕2)=1−cosx ⇒√2+√2+2cos2x=√2×2sin2(
x
2
) As x lies in the 2nd quadrant ⇒√2+√2+2cos2x=2sin(