Question

sin160*cos110+sin250*cos340+tan110*tan340=

Answer 1

Answer:

$sin160\:cos110+sin250\:cos340+tan110\:tan340=0$

Step-by-step explanation:

Formula used:

$sin(A+B)=sinA cosB+cosA sinB$

$CotA=\frac{1}{tanA}$

Now

sin160 = sin(90+70) = cos70

cos110= cos(90+20)= - sin20

sin250 = sin(180+70)= - sin70

cos340 = cos(360-20)= cos20

tan110 = tan(90+20)= - cot20

tan340 = tan(360-20)= - tan20

Now,

$sin160\:cos110+sin250\:cos340+tan110\:tan340$

$=cos70\:(-sin20)+(-sin70)\:cos20+(-cot20)\:(-tan20)$

$=-cos70\:sin20-sin70\:cos20+cot20\:tan20$

$=-(cos70\:sin20+sin70\:cos20)+\frac{1}{tan20}tan20$

$=-(sin70\:cos20+cos70\:sin20)+1$

$=-sin(70+20)+1$

$=-sin90+1$

$=-1+1$

$=0$

Answer 2

Answer:

Sin160°*cos110°+sin250°*cos340°+tan110°*tan340°= 0

Step-by-step explanation:

Sin160°*cos110°+sin250°*cos340°+tan110°*tan340°=

Sin160° = Sin20°

Cos110° = -Cos70°

sin250° = -Sin70°

cos340° = Cos20°

= -Sin20°Cos70° -Sin70°Cos20° -tan70°(-tan20°)

= - (Sin20°Cos70° + Cos20°Sin70°) + tan70°tan20°

= - (Sin(70° + 20°) + 1

= -Sin90° + 1

= -1 + 1

= 0

Sin160°*cos110°+sin250°*cos340°+tan110°*tan340°= 0