If X and Y are complementary angles then show that:

a) sin^2X+sin^2Y=1​

1 thought on “If X and Y are complementary angles then show that:<br /><br />a) sin^2X+sin^2Y=1​”

1. Step-by-step explanation:

   Given :–

   X and Y are complementary angles

   To find:–

   Show that :sin^2X+sin^2Y=1

   Solution:–

   Given that :

   X and Y are the complementary angles

   We know that

   The sum of two angles is equal to 90° then they are complementary angles.

   X+Y = 90°

   => X = 90°-Y

   On taking Sin both sides then

   => Sin X = Sin (90°-Y)

   We know that

   Sin (90°-A) = CosA

   => Sin X = Cos Y

   On squaring both sides then

   => (Sin X)^2 = (Cos Y)^2

   => Sin^2 X = Cos^2 Y

   We know that

   Sin^2 A + Cos^2 A = 1

   => Sin^2 X = 1 – Sin^2 Y

   => Sin^2 X + Sin^2 Y = 1

   Hence, Proved.

   (Or)

   Given that :

   X and Y are the complementary angles

   We know that

   The sum of two angles is equal to 90° then they are complementary angles.

   X+Y = 90°

   => X = 90°-Y

   On taking Cos both sides then

   => Cos X = Cos (90°-Y)

   We know that

   Cos (90°-A) = Sin A

   => Cos X = Sin Y

   On squaring both sides then

   => (Cos X)^2 = (Sin Y)^2

   => Cos^2 X = Sin^2 Y

   We know that

   Sin^2 A + Cos^2 A = 1

   => 1- Sin^2 X = Sin^2 Y

   => Sin^2 X + Sin^2 Y = 1

   Hence, Proved.

   Answer:–

   If X and Y are complementary angles then Sin^2X+Sin^2Y=1

   Used formulae:–

   Complementary angles:–

   • The sum of two angles is equal to 90° then they are complementary angles.

   • Cos (90°-A) = Sin A

   • Sin (90°-A) = CosA

   • Sin^2 A + Cos^2 A = 1

   Reply