Is a triangle such that

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

ABCABC is a triangle such that sin⁡(2A+B)=sin⁡(C−A)=−sin⁡(B+2C)=12\sin(2A+B)=\sin(C-A)=-\sin(B+2C)=\frac{1}{2}. If AA, BB, and CC are in AP, then the values of AA, BB, and CC are (1) 45∘,60∘,75∘45^\circ,60^\circ,75^\circ (2) 30∘,60∘,90∘30^\circ,60^\circ,90^\circ (3) 20∘,60∘,100∘20^\circ,60^\circ,100^\circ (4) None of these

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