What is tan(a-90)sin(-a) ?

The solution to tan(a-90)sin(-a) is cos(a)

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simplify tan(a-90)sin(-a)

simplify

tan (a - 9 0^{\circ}) sin (- a)

cos (a)

Solution steps

tan (a - 9 0^{\circ}) sin (- a)

Use the negative angle identity:

sin (- x) = - sin (x)

= (- sin (a)) tan (- 9 0^{\circ} + a)

Rewrite using trig identities

= (- sin (a)) (- \frac{cos ( a )}{sin ( a )})

Simplify

(- sin (a)) (- \frac{cos ( a )}{sin ( a )}) : cos (a)

= cos (a)

cos (arccos (8 x))

sin (g + π)

sin^{2} (9 0^{\circ} - x)

sin (4 5^{\circ} - x)

cos (arcsin (\frac{x}{a}))