Question

what does property set 1 and property set 2 of trigonometry consists? ​

Answer 1

1.Sin−1(x) = cosec−1(1/x), x∈ [−1,1]−{0}

2 Cos−1(x) = sec−1(1/x), x ∈ [−1,1]−{0}

3.Tan−1(x) = cot−1(1/x), if x > 0 Or,

= cot−1(1/x) −π, if x < 0

4.Cot−1(x) = tan−1(1/x), if x > 0 Or,

= tan−1(1/x) + π, if x < 0

2nd property consists:

1.Sin−1(−x) = −Sin−1(x)

2.Tan−1(−x) = −Tan−1(x)

3.Cos−1(−x) = π − Cos−1(x)

4.Cosec−1(−x) = − Cosec−1(x)

5.Sec−1(−x) = π − Sec−1(x)

6.Cot−1(−x) = π − Cot−1(x)

Answer 2

1.Sin−1(x) = cosec−1(1/x), x∈ [−1,1]−{0}

2 Cos−1(x) = sec−1(1/x), x ∈ [−1,1]−{0}

3.Tan−1(x) = cot−1(1/x), if x > 0 Or,

= cot−1(1/x) −π, if x < 0

4.Cot−1(x) = tan−1(1/x), if x > 0 Or,

= tan−1(1/x) + π, if x < 0

2nd property consists:

1.Sin−1(−x) = −Sin−1(x)

2.Tan−1(−x) = −Tan−1(x)

3.Cos−1(−x) = π − Cos−1(x)

4.Cosec−1(−x) = − Cosec−1(x)

5.Sec−1(−x) = π − Sec−1(x)

6.Cot−1(−x) = π − Cot−1(x)

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