What is the value of sin^2(50)+sin^2(40) ?

The value of sin^2(50)+sin^2(40) is 1

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sin^2(50)+sin^2(40)

sin^{2} (5 0^{\circ}) + sin^{2} (4 0^{\circ})

1

Solution steps

sin^{2} (5 0^{\circ}) + sin^{2} (4 0^{\circ})

Rewrite using trig identities:

sin (5 0^{\circ}) = cos (4 0^{\circ})

sin (5 0^{\circ})

Use the following identity:

sin (x) = cos (9 0^{\circ} - x)

= cos (9 0^{\circ} - 5 0^{\circ})

Simplify

= cos (4 0^{\circ})

= cos^{2} (4 0^{\circ}) + sin^{2} (4 0^{\circ})

Rewrite using trig identities:

1

cos^{2} (4 0^{\circ}) + sin^{2} (4 0^{\circ})

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

= 1

= 1

csc (72 0^{\circ})

- sin (0) sin (π)

\frac{1}{sin ( 9 0 ^{\circ} )}

arctan (- \frac{1}{10})

cos (2 arccos (- \frac{2}{3}))

What is the value of sin^2(50)+sin^2(40) ?
The value of sin^2(50)+sin^2(40) is 1