In , let , , and . Which of the following statements are…

MATHEMATICS · Multi correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

\triangle ABC

, let

a=5

b=4

, and

\cos(A-B)=\frac{31}{32}

. Which of the following statements are correct? (1) The perimeter of

\triangle ABC

equals

\frac{15}{2}

(2) The radius of the circle inscribed in

\triangle ABC

equals

\frac{\sqrt7}{2}

(3) The measure of

\angle C

equals

\cos^{-1}\left(\frac18\right)

(4) The value of

R\left(b^2\sin2C+c^2\sin2B\right)

equals

120