Question

sin square 37 + sin square 53

Answer 1

hey, mate we know that
Sin(37)=3/5
And Sin(53)=Sin(90-37)=Cos(37)=4/5

so Sin²(37)+Sin²(53)=(9/25)+(16/25)

=(16+9)/25
=1

Answer 2

sin² 37° + sin² 53° = 1

Given :

The expression sin² 37° + sin² 53°

To find :

The value of the expression

Formula :

• sin ( 90° - θ ) = cos θ

• sin² θ + cos² θ = 1

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is sin² 37° + sin² 53°

Step 2 of 2 :

Simplify the given expression

sin² 37° + sin² 53°

= sin² 37° + sin² (90° - 37°)

= sin² 37° + cos² 37° [ ∵ sin ( 90° - θ ) = cos θ ]

= 1 [ ∵ sin² θ + cos² θ = 1 ]

∴ sin² 37° + sin² 53° = 1

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