Question

Sen 30° + cos45°=

√2 sen 45° (csc 45° - cos 60°)=

sec^2 30° + cos^2 30°=​

Answer 1

Respuesta:

1. Sen 30° + cos45° =  (1 + √2)/2

2. √2 sen 45° (csc 45° - cos 60°) = (2√2 - 1)/2

3. sec^2 30° + cos^2 30° =​ 25/12

Explicación paso a paso:

1. sen 30° = 1/2

  cos 45° = √2/2

   Sen 30° + cos45° = 1/2 + √2/2 = (1 + √2)/2

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2. sen 45° = √2/2

   csc 45° = 1/sen 45° = 1/(√2/2) = 2/√2 = √2

  √2 sen 45° (csc 45° - cos 60°) = √2 . (√2/2) . (√2 - 1/2)

= 1 . (√2 - 1/2) = (2√2 - 1)/2

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3. sec 30° = 1/ cos 30° = 1(√3/2) = 2/√3)  = 2√3/3

   sec² 30° = (2√3/3)² = (4 . 3)/9 = 4/3

   cos 30° = √3/2

   cos² 30° = (√3/2)² = 3/4

   sec^2 30° + cos^2 30° =​ 4/3 + 3/4 = (16 + 9) /12 = 25/12