Question

2sin32*cos32/sin64=?-6sin32/sin16*sin74=?

Answer 1

1. 2sin32*cos32/sin=  sin96
2.sin106

Answer 2

To solve these trigonometric expressions, let's break them down step by step:

1. 2sin(32°) * cos(32°) / sin(64°):

We'll use the identity sin(2θ) = 2sin(θ)cos(θ) to simplify the expression:

2sin(32°) * cos(32°) / sin(64°) = sin(64°) * cos(32°) / sin(64°) [Using the identity sin(2θ) = 2sin(θ)cos(θ)] = cos(32°)

Therefore, the value of 2sin(32°) * cos(32°) / sin(64°) is equal to cos(32°).

2. -6sin(32°) / sin(16°) * sin(74°):

We can rewrite this expression as follows:

-6sin(32°) / (sin(16°) * sin(74°))

Let's use the identity sin(A - B) = sin(A)cos(B) - cos(A)sin(B) to simplify it further:

-6sin(32°) / (sin(16°) * sin(74°)) = -6sin(32°) / (sin(74° - 16°)) = -6sin(32°) / sin(58°)

Therefore, the value of -6sin(32°) / sin(16°) * sin(74°) is equal to -6sin(32°) / sin(58°).

Note: I have assumed that the angles are measured in degrees, as indicated by the degree symbol (°) in the question.