\tan(a) = 3/4 and \tan (b)=5/12, what is \cos(a+b) Attempt : \cos(a+b)

joygielymmeloiy

joygielymmeloiy

Answered question

2022-01-28

tan(a)=34 and tan(b)=512, what is cos(a+b)
Attempt :
cos(a+b)=cos(a)cos(b)sin(a)sin(b)
And we can write tan(a)=sin(a)cos(a)=0.30.4 and sin(b)cos(b)=0.050.12 so
cos(a+b)=(0.4)(0.12)(0.3)(0.05)=331000
Is this correct?

Answer & Explanation

Johnny Cummings

Johnny Cummings

Beginner2022-01-29Added 7 answers

No, this can't be correct. Remember that sin2x+cos2x=1 for all x; your values for the sine and cosine of a and b do not satisfy this relation.
It turns out that
sina=35cosa=45
sinb=513cosb=1213
and thus
cos(a+b)=cosacosbsinasinb=45121335513=3365

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