Question

Упростить: 2sin^2 a/2+cosa. Доказать тождество: 2sina-sin2a/2sina+sin2a=tg^2a/2. Заменить на произведение: a) sin60(градусов)+sin40(градусов), б) cos5п/12-cosп/12. Помогите, пожалуйста.

Answer 1

1)упростить

sin 2a                      cos a         2sina*cosa         cosa             2sina*cosa       cosa

----------         *     ------------   = -----------------  *  --------------- = ----------------   * ---------- = 2cosa

1+cos a                  1+cos a         sina                    sina                   sina              sina

 

2) доказать тождество

sin 2a                     1-cos 2a                 2sin a

---------------    -    -----------------    =    ------------ = 

sin 3a-sin a           cos a-cos 3a        sin 4a

Answer 2

Simplifying the Expression: 2sin^2(a/2) + cosa

To simplify the expression 2sin^2(a/2) + cosa, we can use trigonometric identities to rewrite it in a different form.

Let's start by using the double-angle identity for sine: sin(2θ) = 2sinθcosθ. We can rewrite the expression as follows:

2sin^2(a/2) + cosa = 2sin(a/2)cos(a/2) + cosa

Next, we can use the Pythagorean identity for sine: sin^2θ + cos^2θ = 1. Rearranging this equation, we get sin^2θ = 1 - cos^2θ. We can substitute this into our expression:

2(1 - cos^2(a/2))cos(a/2) + cosa

Expanding and simplifying further:

**2cos(a/2) - 2cos^3(a/