Question

3 tg² 30° + 4 tg 45° + cos 30° tg 60° С полным решением

Answer 1

Решить $3 tg^2( 30а )+ 4 tg (45а) + cos (30а) * tg (60а)$

Ответ:

$3 tg^2( 30а )+ 4 tg (45а) + cos (30а) * tg (60а)= 3 *(\frac{\sqrt{3} }{3} )^2+4*1+\frac{\sqrt{3} }{2} *\sqrt{3} = 3 * \frac{3}{9} +4+\frac{3}{2} =3 * \frac{1}{3} +4+\frac{3}{2} = 1 +4\frac{3}{2} = 6\frac{1}{2} =6,5$

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ᚨᚾᛏᛁᛋᛈᛁᚱᚨᛚᛋ

Answer 2

To find the value of the expression with the given trigonometric functions, let's break it down step by step.

1. Start with the expression: 3tg²30° + 4tg45° + cos30°tg60°

2. We'll begin by evaluating the trigonometric values for the given angles:

   • tg 30° = sin 30° / cos 30° = (1/2) / (√3/2) = 1/√3
   • tg 45° = sin 45° / cos 45° = (1/√2) / (1/√2) = 1
   • cos 30° = √3/2
   • tg 60° = sin 60° / cos 60° = (√3/2) / (1/2) = √3

3. Substitute these values back into the expression: 3(1/√3)² + 4(1) + (√3/2)(√3)

Simplifying further: 3(1/3) + 4 + √3/2

1 + 4 + √3/2

5 + √3/2

To express this result as a single fraction, we need a common denominator: (10/2) + (√3/2) = (10 + √3) / 2

Therefore, the simplified value of the expression is: (10 + √3) / 2