sin²a+sin²(a+120)+sin²(a-120)=3/2
Answers
Answer:
This above equation can be written as
sin2(120−A)+sin2A+sin2(120+A)
=(sin120∙cosA−cos120∙sinA)2+sin2A+(sin120∙cosA+cos120∙sinA)2
=(√32∙cosA−12∙sinA)2+sin2A+(cosA∙√32+12sinA)2
=2×[34cos2A−14sin2A]+sin2A ____________ [ as (a+b)2+(a−b)2=2×(a2+b2).]
=32cosA2+12sinA2+sinA2
=32cos2A+32sin2A
=32[cos2A+sin2A]
=32■
What is the value of sinA+sin(120+A)+sin(A-120)?
What is the range of function sin^2 (120-x) +sin^2 (120+x)?
What is the minimum value of 2^sin^2A +2^cos^2A?
If sin A= cos A, what is 2 tan^2A + sin^2A -1?
If sinA+sinB+sinC=3 , what is sin2A+sin2B+sin2C ?
sin^2(120-A)+sin^2A+sin^2(120+A)
Weknow that :-
cos2x=1–2sin^2x
or sin ^2x =(1-cos2x)/2
=sin^2(120-A)+sin^2(120+A)+sin^2A.
= {1-cos(240–2A)}/2+{1-cos(240+2A)}/2+ {1- cos2A}/2.
= 1/2.[3- { cos(240-A)°+ cos(240+A)°} -cos2A].
=1/2.[3-{2.cos 240°.cos2A} -cos2A]. , [ cos240°=cos(180+60)° =-cos60° = -1/2].
=1/2.[3–2. (-1/2).cos2A- cos2A].
=1/2.[3+cos2A -cos2A].
= 3/2. Answer.
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Ans: 3/2
What is the value of sinA+sin(120+A)+sin(A-120)?
What is the range of function sin^2 (120-x) +sin^2 (120+x)?
What is the minimum value of 2^sin^2A +2^cos^2A?
If sin A= cos A, what is 2 tan^2A + sin^2A -1?
If sinA+sinB+sinC=3 , what is sin2A+sin2B+sin2C ?
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Answer:
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