Question

Sin74°×ctg53°+cos74°​

Answer 1

$sin74^o\cdot cgt53^o+cos74^o=$

$sin(2\cdot37^o)\cdot\frac{cos53^o}{sin 53^o}+cos(2\cdot37^o)=$

$2sin37^o cos37^o\cdot\frac{cos(90^o-37^o)}{sin(90^o-37^o)}+1-2sin^237^o=$

$2sin37^o cos37^o\cdot\frac{sin37^o}{cos37^o}+1-2sin^237^o=$

$2sin^237^o-2sin^237^o=1$

Answer 2

To calculate the value of the expression Sin(74°) × ctg(53°) + cos(74°), we first need to determine the values of sine, cotangent, and cosine for the given angles.

1. Sin(74°): Using a calculator, we find that Sin(74°) is approximately 0.9613.

2. ctg(53°) (cotangent of 53°): The cotangent of an angle is the reciprocal of the tangent. So, ctg(53°) = 1 / tan(53°). Using a calculator, we find that tan(53°) is approximately 1.3270. Therefore, ctg(53°) ≈ 1 / 1.3270 ≈ 0.7536.

3. Cos(74°): Using a calculator, we find that Cos(74°) is approximately 0.2393.

Now, we can substitute these values into the expression:

Sin(74°) × ctg(53°) + cos(74°) ≈ 0.9613 × 0.7536 + 0.2393

Now, calculate the values:

0.9613 × 0.7536 ≈ 0.7245 0.7245 + 0.2393 ≈ 0.9638

So, Sin(74°) × ctg(53°) + cos(74°) ≈ 0.9638 (rounded to four decimal places).