Question

Sin(П-a)ctg(3п/2+a)/tg(2п-a)cos(п/ 2-a)

Answer 1

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Answer 2

To simplify this expression, we can use trigonometric identities to rewrite each trigonometric function in terms of sine and cosine.

sin(π - a) = sin π cos a - cos π sin a = 0 cos a - (-1) sin a = sin a ctg(3π/2 + a) = 1 / tan(3π/2 + a) = 1 / (-cot a) = -tan a tg(2π - a) = -tan a cos(π/2 - a) = cos π/2 cos a + sin π/2 sin a = 0 cos a + 1 sin a = sin a

Substituting these identities into the original expression, we get:

sin a (-tan a) / (-tan a) sin a

Canceling out the common factors of sin a and tan a, we are left with:

-1

Therefore, the simplified expression is -1.