Question

if a = sin‐¹x + cos‐¹x — tan‐¹x , x>=0, then smallest interval in which a lies is given​

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: