Express sin –1 x in terms of (i) cos –1 
(ii) tan –1 
(iii) cot –1 
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) sin –1 x = 
(ii) sin –1 x = tan –1 
, for all x ∈ (–1, 1)
(iii) sin –1 x = 
Sol. (i) Let sin –1 x = θ . Then x = sin θ and – 
≤ θ ≤ 
∴ cos θ = 
= 
cos –1 
= cos –1 (cos θ ) = 
= 
∴ sin –1 x = 
(ii) Let sin –1 x = θ . Then x = sin θ and 
{Note : θ ≠ 
, 
because x ≠ ± 1 }
∴ tan θ = 
= 
∴ tan –1 
= tan –1 (tan θ ) = θ = sin –1 x
Thus sin –1 x = tan –1 
, for all x ∈ (–1, 1)
(iii) Let sin –1 x = θ . Then x = sin θ and 
or 
{ Note : θ ≠ 0 , because x ≠ 0 }
∴ cot θ = 
∴ cot –1 
= cot –1 (cot θ ) = 
= 
Thus sin –1 x = 
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