Question

(a) Prove that:

arccos z = −i log (= + i(1 − 2²)³¹)

(b) Solve the equation cosz=3/4i

Answer 1

cos

−1

x+cos

−1

y+cos

−1

z=π

cos

−1

x+cos

−1

y=π−cos

−1

z

cos

−1

(xy−

1−x

2

​

1−y

2

​

)=π−cos

−1

z

xy−

1−x

2

​

1−y

2

​

=cos(π−cos

−1

z)

xy−

1−x

2

​

1−y

2

​

=−cos(cos

−1

z)

xy−

1−x

2

​

1−y

2

​

=−z

xy+z=

1−x

2

​

1−y

2

​

(xy+z)

2

=(1−x

2

)(1−y

2

)

x

2

y

2

+z

2

+2xyz=1−x

2

−y

2

+x

2

y

2

x

2

+y

2

+z

2

+2xyz=1