What is the value of (sin(45))^2+(cos(45))^2 ?

The value of (sin(45))^2+(cos(45))^2 is 1

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(sin(45))^2+(cos(45))^2

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

1

Solution steps

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

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

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

= (\frac{2}{2})^{2} + (\frac{2}{2})^{2}

Simplify

(\frac{2}{2})^{2} + (\frac{2}{2})^{2} : 1

= 1

8 cos (30 0^{\circ})

sin (8 0^{\circ}) csc (8 0^{\circ})

80 cos (2 0^{\circ})

sin (- \frac{13 π}{4})

sec (arctan (\frac{2}{5}))

What is the value of (sin(45))^2+(cos(45))^2 ?
The value of (sin(45))^2+(cos(45))^2 is 1