Inverse trignometry

Q1 If cos^-1Î» +cos^-1Î¼ +cos^-1Î½=3Ï€ then prove that Î»Î¼+Î¼Î½+Î»Î½=3

Q2 If ²ⁿÎ£_i=1 sin^-1x_i=nÏ€ then prove that ²ⁿÎ£_i=1x_i=2n

1 Answers

Question 1)

the limit on cos inverse says that each of the three cos inverses is pi

hence cos^-1Î» = Ï€

Thus, Î»=Î¼=Î½=-1

Thus the identity Î»Î¼+Î¼Î½+Î»Î½=3

Question 2) Use the same logic as in 1 to prove taht x_i=1

Hence²ⁿÎ£_i=1x_i=2n

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