Question

Cos(90°-a)+sin(180°+a)tg(90°+a)tg a

Answer 1

Sina+sinactgatga=sina+sina*cosa/sina*sina/cosa=2sina

Answer 2

To simplify the given expression, let's break it down step by step:

1. Recall the trigonometric identities:

   • cos(90° - a) = sin(a)
   • sin(180° + a) = -sin(a)
   • tan(90° + a) = -cot(a) (cotangent is the reciprocal of tangent, so cot(a) = 1/tan(a))

2. Substitute the identities into the expression: cos(90° - a) + sin(180° + a) * tan(90° + a) * tan(a) = sin(a) + (-sin(a)) * (-cot(a)) * tan(a) = sin(a) - sin(a) * (-cot(a)) * tan(a)

3. Simplify further: Recall that tan(a) = sin(a) / cos(a), and cot(a) = 1 / tan(a) = cos(a) / sin(a). Therefore, (-cot(a)) * tan(a) = (-cos(a)/sin(a)) * (sin(a)/cos(a)) = -1.

   The expression becomes: sin(a) - sin(a) * (-1) = sin(a) + sin(a) = 2 * sin(a)

So, the simplified expression is 2 * sin(a).