Question

sin 160°cos110°+sin 250°cos340°+tan 110tan 340°​

Answer 1

Answer:

0

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Step-by-step explanation:

sin(A+B)=sinAcosB+cosAsinB

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

tanA

1

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\:tan340sin160cos110+sin250cos340+tan110tan340

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

=-cos70\:sin20-sin70\:cos20+cot20\:tan20=−cos70sin20−sin70cos20+cot20tan20

=-(cos70\:sin20+sin70\:cos20)+\frac{1}{tan20}tan20=−(cos70sin20+sin70cos20)+

tan20

1

tan20

=-(sin70\:cos20+cos70\:sin20)+1=−(sin70cos20+cos70sin20)+1

=-sin(70+20)+1=−sin(70+20)+1

=-sin90+1=−sin90+1

=-1+1=−1+1

=0=0