1.PROVE Sin3x/Sinx-Cos3x/Cosx=2?2.IF tanA=1/2 , tanB=1/3 and A,B are acute angles, find A+B
SURYA VAMSI , 7 Years ago
Grade 11
Trigonometry> 1.PROVE Sin3x/Sinx-Cos3x/Cosx=2? 2.IF tan...
1 Answers
Prashant
Last Activity: 7 Years ago
Sol1. We know that Sin3x= 3Sinx-4(Sinx)^3
and Cos3x=4(Cosx)^3- 3Cosx
hence the given expression Sin3x/Sinx-Cos3x/Cosx = (3Sinx-4(Sinx)^3)/Sinx-(4(Cosx)^3- 3Cosx)/Cosx
= 3- 4(Sinx)^2- 4(Cosx)^2 +3
= 6- 4{(Sinx)^2+(Cosx)^2}
= 6- 4 =2 {since (Sinx)^2+(Cosx)^2 =1; an identity}
Sol2. tanA=1/2, tanB=1/3 find A+B
we know that tan(A+B)= (tanA +tanB)/(1- tanA * tanB)
using above identity we have :
tan(A+B)=(1/2 + 1/3)/(1-(1/2 *1/3) = (5/6)/(5/6) =1
tan(A+B)=1
A+B=arc tan(1)=45 degrees
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