How do you show that sin(x+60) + sin(x+120) =(√3)cosx ?

2 Answers
Sunayan S
Feb 28, 2018

See the answer below...

Explanation:

sin(x+60)+sin(x+120)

=2 cdot sin{((x+60)+(x+120))/2} cdot cos{((x+60)-(x+120))/2}

=2 cdot sin{(2x+180)/2} cdot cos{(-60)/2}

=2 cdot sin{90+x} cdot cos{30}

=2 cdot sin{90-(-x)} cdot cos30

=2 cdot cosx cdot sqrt3/2

=sqrt3 cdot cosx

Shreya
Feb 28, 2018

see below

Explanation:

We have,sin(x+60) +sin(x+120) on L.H.S
According to formula, sin(a+b)=sinacosb+cosasinb
Applying it,we get,
sinxcos(60) +cosxsin(60) +sinxcos(120) + cosxsin(120)
or, sinx//2 +cosx xx (sqrt3)//2 -sinx//2 +cosx xx(sqrt3)//2
{color(blue)(as cos "120 " is -1//2 and sin "120 " is (sqrt3)//2}

Thus,the expression comes out to be,2xx (sqrt3)//2 xxcosx which is color(red)(sqrt3 cosx), the R.H.S

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