Question

if Q= sin^-1X + cos^-1X then the smallest interval in which Q lies​

Answer 1

Answer:

Given 0≤x≤1⟹tan

−1

x∈[tan

−1

0,tan

−1

1]⟹tan

−1

x∈[0,

4

π

]⟹−tan

−1

x∈[−

4

π

,0]

θ=sin

−1

x+cos

−1

x−tan

−1

x=

2

π

−tan

−1

x (∵sin

−1

x+cos

−1

x=

2

π

)

As −tan

−1

x∈[−

4

π

,0]

⟹

2

π

−tan

−1

x∈[

4

π

,

2

π

]

⟹

4

π

≤θ≤

2

π

Step-by-step explanation:

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Answer 2

Answer:

Given 0≤x≤1⟹tan

−1

x∈[tan

−1

0,tan

−1

1]⟹tan

−1

x∈[0,

4

π

]⟹−tan

−1

x∈[−

4

π

,0]

θ=sin

−1

x+cos

−1

x−tan

−1

x=

2

π

−tan

−1

x (∵sin

−1

x+cos

−1

x=

2

π

)

As −tan

−1

x∈[−

4

π

,0]

⟹

2

π

−tan

−1

x∈[

4

π

,

2

π

]

⟹

4

π

≤θ≤

2

π