Evaluation: Tan 70 ° cos10 ° + 3 * sin 10 ° Tan 70 ° - 2cos40 ° under Radix

Evaluation: Tan 70 ° cos10 ° + 3 * sin 10 ° Tan 70 ° - 2cos40 ° under Radix

Tan 70 ° cos10 ° + 3 * sin 10 ° Tan 70 ° - 2cos40 ° under root sign
=cot20°cos10°+√3sin10°tan70°-2cos40°
=cos10°cos20°/sin20°+√3sin10°sin70°/cos70°-2cos40°
=cos10°cos20°/2sin10°cos10°+√3sin10°cos20°/sin20°-2cos40°
=cos20°/2sin10°+√3sin10°cos20°/2sin10°cos10°-2cos40°
=cos20°/2sin10°+√3cos20°/2cos10°-2cos40°
=(cos10°cos20°+√3sin10°cos20°)/2sin10°cos10°-2cos40°
=2cos20°(√3sin10°/2+cos10°/2)/sin20°-2cos40°
=2cos20°(sin10°cos30°+cos10°sin30°)/sin20°-2cos40°
=2cos20°sin40°/sin20°-2cos40°
=4sin20°cos²20°/sin20°-2cos40°
=4cos²20°-2cos40°
=2(2cos²20°-1)-2cos40°+2
=2cos40°-2cos40°+2
=2

tan70°•cos10°（ 3tan20 ° - 1) is equal to () A. 1 B. 2 C. -1 D. -2

Tan70 ° cos10 ° (3tan20 ° - 1) = sin70 ° cos70 ° cos10 ° (3 · sin20 ° cos20 ° - 1) = cos20 ° cos10 ° sin20 ° - 3sin20 ° cos20 ° = cos10 ° sin20 °× 2Sin (20 ° - 30 °) = - sin20 ° sin20 ° = - 1

(1-2sin10cos10) / (cos10 - (1-cos ^ 2 170) Basic elementary function, high one. Detailed

√(1-2sin10cos10)=√(sin^2 10+cos^2 10-2sin10cos10)=√(sin10-cos10)^2=cos10-sin10
cos170=-cos10.
√(1-cos^2 170)=√(1-cos^2 10)=√sin^2 10=sin10
The original formula = (cos10-sin10) / (cos10-sin10) = 1

Calculation: Tan 70 ° cos10 ° (Radix 3 · Tan 20 ° - 1)

Cut to string
tan70°cos10°（√3·tan20°-1）
=Sin70cos10 / cos70 [√ 3sin20-cos20) / cos20] can be obtained by the general division
=Conversion of cosine to cosine of cos20cos10 / sin20 [√ 3sin20-cos20) / cos20]
=Cos10 / sin20 * 2 [√ 3xin20 / 2-1 / 2cos20] reduction + common factor
=cos10/sin20 *2（cos30sin20-sin30cos20）
=cos10/sin20 *2sin（-10）
=cos10/sin20 *（-2）sin10
=（-2）sin10cos10/sin20
=-1

Trigonometric identity transformation problem: simplification: Tan 70 ° cos10 ° (√ 3 Tan 20 ° - 1) Note: √ 3 is the radical 3 The process should not be too simple

tan70°*cos10°*(√3 *tan20° -1)
=tan70°*cos10°*(tan60 °*tan20° -1)
=tan70°*cos10°*[(sin60 °*sin20°/cos60°*cos20°)-1]
=tan70°*cos10°*(sin60 °*sin20°-cos60°*cos20°)/(cos60 °*cos20°)
=tan70°*cos10°*[-cos(60°+20°)]/(cos60 °*cos20°)
=-tan70°*cos10°*cos80°/(cos60 °*cos20°)
=-tan70°*cos10°*sin10°/(cos60 °*cos20°)
=-(sin70°/cos70°)*(1/2)*sin20°/(cos60 °*cos20°)
=-(cos20°/sin20°)*sin20°/(2cos60 °*cos20°)
=-1/(2cos60 °)
=-1
tan70°cos10°（√3 tan20°-1）
=2cot20°cos10°[√3 (sin20°/ cos20° )-1]
=2cot20°cos10°（√3/2 sin20°-1/2 cos20°）(1 /cos20°)
=2(cos20°/sin20°) cos10°（sin20°cos30°-cos20°sin30°）(1/ cos20°)
=-2sin10°cos10° /sin20°
=-1

(1) Sin40 degree (TA N10 degree - root 3) (2) Tan 70 degree cos10 degree (3 * Tan 20 degree - 1) how to simplify these two?

(1) sin40(sin10/cos10 - sin60/Cos60)
=Sin40/(Cos10Cos60) (Sin 10 Cos60 - Cos10Sin60)
=Sin40 Sin (-50)/ (Cos10 Cos60)
=-Sin40 Cos40 / (Sin80 Cos 60)
= - Sin80/ 2 /(Sin80 Cos 60)
= - 1/(2Cos60)
=-1
(2)Sin70/Cos70 Cos10 * (Sin 60/Cos60 Sin20 /Cos20 -1)
= Cos20 Cos 10/Cos70 *(Sin60 Sin20 - Cos60 Cos20)/ (Cos60 Cos20)
= Cos10 /Cos70 * (-Cos40) / Cos60
= - Cos 10 Cos40 /(Cos70 Cos60)
= - 2 Sin80 Cos40/ Sin 20
= - 8 sin20 Cos 20 Cos40 /Sin20
= -8 Cos20 Cos40
=-4 (Cos 20 - Cos (60)]
= -4 Cos 20 +2

Simplified Tan 70 ° cos10 ° (√ 3tan20 ° - 1) One more: sin50°(1+√3tan10°)

tan70cos10(√3tan20-1)
=2cot20cos10(√3sin20/cos20-1)
=2cot20cos10(√3/2sin20-1/2cos20)/cos20
=2(cos20/sin20)cos10(sin20cos30-cos20sin30)/cos20
=(2/sin20)cos10sin(20-30)
=(-2sin10cos10)/sin20
=-1
sin50(1+√3tan10)
=sin50(1+tan60tan10)
=sin50[1+(sin60/cos60)*(sin10/cos10)]
=sin50[1+(sin60*sin10)/(cos60*cos10)]
=sin50[(sin10*sin60+cos10*cos60)/(cos10*cos60)]
=sin50[cos(60-10)/(cos10*cos60)]
=sin50[cos50/(cos10*cos60)]
=(sin50*cos50)/(cos10*cos60)
=sin100/(2*cos10*cos60)
=sin80/(2*cos10*cos60)
=cos10/(2*cos10*cos60)
=1/(2cos60)
=1

Evaluation: Tan 70 degrees * cos 10 degrees * (root 3 Tan 20 degrees - 1)

tan70°*cos10°*(√3 *tan20° -1)
=tan70°*cos10°*(tan60 °*tan20° -1)
=tan70°*cos10°*[(sin60 °*sin20°/cos60°*cos20°)-1]
=tan70°*cos10°*(sin60 °*sin20°-cos60°*cos20°)/(cos60 °*cos20°)
=tan70°*cos10°*[-cos(60°+20°)]/(cos60 °*cos20°)
=-tan70°*cos10°*cos80°/(cos60 °*cos20°)
=-tan70°*cos10°*sin10°/(cos60 °*cos20°)
=-(sin70°/cos70°)*(1/2)*sin20°/(cos60 °*cos20°)
=-(cos20°/sin20°)*sin20°/(2cos60 °*cos20°)
=-1/(2cos60 °)
=-1/4

3.3 the value of {1 - (COS ^ 2) 170} under the root sign (1-2sin10 degree cos10 degree) / cos10 radical sign is_____ .

One
The solution process: under the molecular root (1-2sin10 degree cos10 degree) = under the root sign (sin ^ 10 degree + cos ^ 10 degree - 2sin10 degree cos10 degree) = under the root sign (sin10 degree - cos10 degree) ^ = cos10 degree - sin10 degree
The root must be positive, cos 10 is larger than sin 10
Denominator cos10 degree - under root sign {1 - (COS ^ 2) 170 degree = cos10 degree - Sin ^ 170 degree = cos10 degree - (- Sin 170 degree) = cos10 degree + sin 170 degree = cos10 degree - Sin 10 degree
So the final ratio is 1

Under root sign (1-2sin10 degree cos10 degree) / under root sign (1-cos170 degree square - cos350 degree)

Under the root sign ((cos10-sin10)) / under the root sign (1 + cos10-cos10)
=cos10-sin10
=Root sign (2) * cos55