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19. Range of the function \( f(x)=\frac{1}{\cos \left(\sin ^{-1}(\sin x+\cos x)\right\}} \) is (A) \( [-1,1]-\{0\} \) (B) \( (-\infty,-1] \cup[1, \infty) \) (C) \( (0,1] \) (D) \( (1, \infty) \)Ans.D |
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Answer» range of (sin x + cos x ) is [ -√2 ,+√2] but the domain of sin-1 x is limited to [-1,+1] so range of function sin-1 is[-π/2 ,+π/2] this means domain of func cosine will be [-π/2 ,+π/2] So range of cosine function would be [0,1] and range of F(x) will be [1 , infinity) hence D option |
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