What is the value of sin^2(30)+cos^2(60)-1 ?

The value of sin^2(30)+cos^2(60)-1 is -1/2

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sin^2(30)+cos^2(60)-1

sin^{2} (3 0^{\circ}) + cos^{2} (6 0^{\circ}) - 1

- \frac{1}{2}

Solution steps

sin^{2} (3 0^{\circ}) + cos^{2} (6 0^{\circ}) - 1

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

= (\frac{1}{2})^{2} + (\frac{1}{2})^{2} - 1

Simplify

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

= - \frac{1}{2}

csc^{2} (\frac{2 π}{3})

1 \cdot sin (6 0^{\circ})

\frac{6}{tan ( 3 9 ^{\circ} )} + \frac{6}{tan ( 4 4 ^{\circ} )}

cos (1 0^{\circ}) + sin (8 0^{\circ})

(520) cos (4 5^{\circ})

What is the value of sin^2(30)+cos^2(60)-1 ?
The value of sin^2(30)+cos^2(60)-1 is -1/2