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

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

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2cos^2(157.5)-1

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

\frac{2}{2}

Solution steps

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

Rewrite using trig identities:

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

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

Simplify

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

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}

sin (\frac{2 π}{7})

cos (- \frac{11 π}{3})

- sin (\frac{4 π}{3})

sin (10 6^{\circ})

3 \cdot csc (3 7^{\circ})

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