If Tan α = 2, find sin ^ 2 α + sin α * cos α + 3cos ^ 2 α =?

If Tan α = 2, find sin ^ 2 α + sin α * cos α + 3cos ^ 2 α =?

Since sin α / cos α = 2, sin α = 2cos α
Bring in sin ^ 2 α + sin α * cos α + 3cos ^ 2 α = 9cos ^ 2 α
And because sin ^ 2 α + cos ^ 2 α = 1, we get the solution
cos^2α=1/5
So the original formula is 9 / 5

tan10°*tan30°+ tan30°* tan50°+ tan10°*tan50°
Need to simplify process

tan10°*tan30°+ tan50°*（tan30°+ tan10° ）
=tan10°*tan30°+ cot40°*（tan30°+ tan10° ）
=tan10°*tan30°+ [(1-tan10°*tan30°)/(tan30°+ tan10°)]*（tan30°+ tan10° ）
=tan10°*tan30°+ 1-tan10°*tan30°
=1

tan30+tan40+tan50+tan60=?
Simplify the formula

For tan30.tan60, we don't need to discuss the main research → tan40 + tan50 = Tan (30 + 10) + Tan (60-10) = {(cos10 + √ 3 * sin10) / (√ 3 * cos10-sin10)} + {(√ 3 * cos10-sin10) / (cos10 + √ 3 * sin10)} = {(1 + 2sin10 ^ 2 + √ 3 * sin20 + 1 + 2cos10 - √ 3 * sin20)} /

Simplification (3 + Tan 30 ° Tan 40 ° + Tan 40 ° Tan 50 ° + Tan 50 ° Tan 60 °) cot 80 °

Cot80 = tan10 = (tan40-tan30) / (1 + tan30 * tan40), so: (1 + tan30 * tan40) * tan10 = tan40-tan30
Similarly: (1 + tan40 * tan50) * tan10 = tan50-tan40
(1+tan50*tan60)*tan10=tan60-tan50
So:
（3+tan30*tan40+tan40*tan50+tan50*tan60)*tan10
=(1+tan30*tan40)*tan10+(1+tan40*tan50)*tan10+(1+tan50*tan60)*tan10
=(tan40-tan30)+(tan50-tan40)+(tan60-tan50)
=tan60-tan30
=√3-(1/3)√3
=(√2/3）√3
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sin50(1+√3tan10)+tan10+tan50+√3tan10tan50

tan(10+50)=(tan10+tan50)/(1-tan10tan50)=√3 tan10+tan50+√3tan10tan50=√3 tan(60-10)=(tan60-tan10)/(1+tan60tan10) 1+√3tan10=1+tan60tan10=(tan60-tan10)/tan50 sin50(1+√3tan10)=(tan60-tan10)cos50=(sin6...

Calculate | 3-2 | - 12 × Tan 60 ° + 2cos 30 ° + (12) - 1

The original formula is 2-3-23 × 3 + 2 × 32 + 2 = - 2

The results of Tan 60 ° + 2 sin 45 ° - 2 cos 30 °

Radical 3 + 2 * radical 2 / 2-2 * radical 3 / 2

Calculation: tan60 ° + 2sin45 ° - 2cos30 °

Original formula = 3 + 2 × 22-2 × 32 (3 points) = 3 + 2-3 = 2. (5 points)

|Tan45 ° - tan60 ° | + √ sin ^ 260 ° - 2cos30 ° + 1, why is it a double root sign

|tan45°-tan60°|+√sin^260°-2cos30°+1
=|1-√3|+sin60°-2*√3/2+1
=√3-1+√3/2-√3+1
=√3/2

4sin 30: Tan 60 divided by sin 2 45 minus 2cos 30. It's best to type it in Chinese. Thank you

This is very simple: sin30 = 1 / 2, sin45 = root 2 / 2, tan60 = root 3, cos30 = root 3 / 2, root 3 / (1 / 2-2 * root 3 / 2) / 4 * 1 / 2 = root 3 / 4-3 / 2 = 0.433-1.5 = -0.767