What is cos(arcsin(-cos(x))) ?

The solution to cos(arcsin(-cos(x))) is sqrt(sin^2(x))

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simplify cos(arcsin(-cos(x)))

simplify

cos (arcsin (- cos (x)))

sin^{2} (x)

Solution steps

cos (arcsin (- cos (x)))

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

= 1 - (- cos (x))^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- cos (x))^{2} = cos^{2} (x)

= 1 - cos^{2} (x)

Rewrite using trig identities

= sin^{2} (x)

sec (arctan (\frac{x}{4}))

tan (x + x)

3 - 2 sin^{2} (x)

tan (27 0^{\circ} - θ)

cos (π - 2 x)

What is cos(arcsin(-cos(x))) ?
The solution to cos(arcsin(-cos(x))) is sqrt(sin^2(x))