The direction angles made by a line ' L ’ with the coordinate axes, are α,β,γ.  Then the range of sin2α+sin2β

Ifα,β,γ are the angles made by a line ‘L’ with the coordinate axes in the positive direction thencos2α+cos2β+cos2γ=1It implies that 1−sin2α+1−sin2β+1−sin2γ=1⇒sin2α+sin2β+sin2γ=2Hence, sin2α+sin2β=2−sin2γThe minimum value of sin2γis zero and its maximum value is 1So that the range of  sin2α+sin2βis 1,2