What is the value of 1-2sin^2(157.5) ?

The value of 1-2sin^2(157.5) is (sqrt(2))/2

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1-2sin^2(157.5)

1 - 2 sin^{2} (157. 5^{\circ})

\frac{2}{2}

Solution steps

1 - 2 sin^{2} (157. 5^{\circ})

Rewrite using trig identities:

sin (157. 5^{\circ}) = sin (22. 5^{\circ})

= 1 - 2 sin^{2} (22. 5^{\circ})

Rewrite using trig identities:

cos (4 5^{\circ})

= cos (4 5^{\circ})

Use the following trivial identity:

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

= \frac{2}{2}

csc (arctan (- \frac{3}{3}))

arcsin (\frac{7}{12})

sin (\frac{15}{17})

arctan (\frac{15}{20})

cos (7 6^{\circ})

What is the value of 1-2sin^2(157.5) ?
The value of 1-2sin^2(157.5) is (sqrt(2))/2