Question

Sina cos2a -cos(-a)sin(-2a)

Answer 1

SinαCos2α - Cos(- α)Sin(- 2α) = SinαCos2α + CosαSin2α =

= Sin(α + 2α) = Sin3α

Cos(- α) = Cosα

Sin(- 2α) = - Sin2α

Answer 2

Упростить выражение, используя свойства чётности или нечётности тригонометрических функций:

sin(a)cos(2a)-cos(a)(-sin(2a));

Произведение двух отрицательных значений положительно(минус на минус даёт плюс):

sin(a)cos(2a)+cos(a)sin(2a);

Упростить выражение, используя формулу sin(t)cos(s)+cos(t)sin(s)=sin(t+s):

sin(3a)

Answer 3

To simplify the expression Sina cos2a - cos(-a)sin(-2a), let's break it down step by step using trigonometric identities:

1. Recall the even/odd properties of trigonometric functions:

   • cos(-x) = cos(x) (even function)
   • sin(-x) = -sin(x) (odd function)

2. Apply the even/odd properties to simplify the expression:

   • cos(-a) = cos(a)
   • sin(-2a) = -sin(2a)

3. Substitute the simplified expressions back into the original expression: Sina cos2a - cos(-a)sin(-2a) = Sina cos2a - cos(a)(-sin(2a))

4. Apply the double angle identity for cosine: cos(2a) = cos^2(a) - sin^2(a)

5. Substitute the double angle identity into the expression: Sina cos2a - cos(a)(-sin(2a)) = Sina (cos^2(a) - sin^2(a)) - cos(a)(-sin(2a))

6. Expand the expression: Sina (cos^2(a) - sin^2(a)) - cos(a)(-sin(2a)) = Sina cos^2(a) - Sina sin^2(a) + cos(a)sin(2a)

Thus, the simplified expression is Sina cos^2(a) - Sina sin^2(a) + cos(a)sin(2a).