Solution process of (1 + radical 3 × tan10) cos40

Solution process of (1 + radical 3 × tan10) cos40

cos40（1+√3tan10）
=cos40[1+(cos30/sin30)*(sin10/cos10)]
=cos40(sin30cos10+cos30*sin10)/sin30cos10
=(cos40sin40)/sin30cos10
=2(cos40sin40)/cos10
=sin80/cos10
=sin80/sin80
=1
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How to calculate cos40?

Original style = cos40 ° * ((root 3sin10 ° + cos10 °) / cos10 °)
= cos40°（2cos（60°-10°）/ cos10°）= 2cos40°cos50°/ cos10°
> = 2sin50°cos50°/ cos10°
= sin100°/ cos10°
= cos10°/ cos10°
= 1

Simplification evaluation: sin50 degree [1 + (radical 3) Tan 10 degree]

Sin 50 degree [1 + (radical 3) Tan 10 degree]
=sin50(cos10+√3sin10)/cos10
=sin50*2sin(10+30)/cos10
=2sin50sin40/cos10
=2sin50cos50/cos10
=sin100/cos10
=sin80/cos10
=cos10/cos10
=1

Simplification with trigonometric ratio formula: sin50 '(1 + radical 3 * tan10')

Method 1: sin 50 ° (1 + √ 3 × Tan 10 °) = (sin 50 ° cos10 ° + √ 3sin50 ° sin10 °) / cos10 ° = [sin (60 ° - 10 °) cos10 ° + √ 3sin (60 ° - 10 °) sin 10 °] / cos10 ° = (sin 60 ° cos10 ° - cos 60 ° sin 10 ° cos 10 ° + √ 3sin60 ° C

Simplify (Tan 10 degree radical 3) cos (10 degree) / sin 50 degree

－2

First simplify, in the evaluation: (a-radical 3) multiply (a + radical 3) - A (a-6), where a = root 5 + 1 / 2

(a-radical 3) times (a + radical 3) - A (a-6)
=a^2-(√3^2)-a^2+6a
=6a-3
When a = √ 5 + 1 / 2, the original formula = 6 * (√ 5 + 1 / 2) = 3 + 6 √ 5

The second root sign, (calculation in question 1) radical 18 * Radix 20 * Radix 75, (2) Radix 3 ^ 2 * 4 ^ 3 * 5 (3) simplification, Radix 300

（1）√18×√20×√75=（3√2）×（2√5）×（5√3）=3×（√2）×2×（√5）×5×（√3）=（3×2×5）×（√2×√5×√3）=30√30（2）√3²×5³×5=√3²×5^4=3×5×5=75（3）√300=√10×10×3=10...

2 times of root sign 3 + 2 / 2 root sign, 5-10 times root sign 0.04 (accurate to 0.01) how to calculate the process;

2√3+√5/2-10√0.04
=2√3+√5/2-10*0.2
=2*1.732+2.236/2-2
=3.464+1.118-2
=2.582
=2.58

How to simplify Radix (9-4 times Radix 5)?

√（9-4√5）
= √（√5²-2×2×√5+2²）
= √（√5-2）²
= √5-2

Find the radian, sin, cos, Tan of the following special angles 30，45，60，90，120，135，150，180，210，225，240，270，300，330，360

Angle sin cos Tan
0 0 1 0
30 1 / 2 roots 3 / 2 roots 3 / 3
45 roots 2 / 2 roots 2 / 2 1
60 root number 3 / 2 1 / 2 root number 3
90 10 does not exist
120 root 3 / 2 - 1 / 2 - root 3
135 root 2 / 2 - root 2 / 2 - 1
150 1 / 2 - root 3 / 2 - root 3 / 3
180 0 -1 0
210 - 1 / 2 - root 3 / 2 root 3 / 3
2 / 2-225
240 - root 3 / 2 - 1 / 2 root 3
270 - 10 does not exist
300 - root 3 / 2 1 / 2 - root 3
330 - 1 / 2 root 3 / 2 - root 3 / 3
360 0 1 0
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