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Graph Of Inverse Trignometric Function (त्रिकोणमितीय प्रतिलोम के आरेख)|Inverse Trigonometric Function (प्रतिलोम त्रिकोणमितीय फलन)|Properties Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमितीय फलन के गुणधर्म)|Questions (प्रश्न)|Summary

Inverse Functions (प्रतिलोम फलन)|Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमितीय फलन)|Questions|Properties of Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमितीय फलन के गुणधर्म)|Questions|OMR

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Class 12 Maths Most Important Questions | Inverse Trigonometric Functions | NCERT

Properties of Inverse Trigonometric Functions (प्रतिलोम त्रिकोणमितीय फलन के गुणधर्म)|Questions|OMR

Maximum & Minimum Value of Trigonometric Function (त्रिकोणमिति फलन के उच्चतम एवं निम्नतम मान)|Trigonometrical Equations with their General Solution (त्रिकोणमितीय समीकरण उनके सामान्य हल)|Practice Questions (अभ्यास प्रश्न)|OMR

For any positive integer n , define f_n :(0,oo)rarrR as f_n(x)=sum_(j=1)^ntan^(-1)(1/(1+(x+j)(x+j-1))) for all x in (0, oo) . Here, the inverse trigonometric function tan^(-1)x assumes values in (-pi/2,pi/2)dot Then, which of the following statement(s) is (are) TRUE? sum_(j=1)^5tan^2(f_j(0))=55 (b) sum_(j=1)^(10)(1+fj '(0))sec^2(f_j(0))=10 (c) For any fixed positive integer n , (lim)_(xrarroo)tan(f_n(x))=1/n (d) For any fixed positive integer n , (lim)_(xrarroo)sec^2(f_n(x))=1

cos^(-1) (cos (-5)) + sin^(-1) (sin(6)) - tan^(-1)(tan (12)) is equal to : (The inverse trigonometric functions take the principal values)

cos^(-1) (cos (-5)) + sin^(-1) (sin(6)) - tan^(-1)(tan (12)) is equal to : (The inverse trigonometric functions take the principal values)

Let E_1={x in R : x!=1 and x/(x-1)gt0} and E_2={x in E_1:sin^(-1)((log)_e(x/(x-1))) is a real number} . Here, the inverse trigonometric function sin^(-1)x assumes values in [pi/2,pi/2] Let f: E_1->R be the function defined by f(x)=(log)_e(x/(x-1)) and g: E_2->R be the function defined by g(x)=sin^(-1)((log)_e(x/(x-1))) LIST-I LIST-II P. The range of f is 1. (-oo,1/(1-e)]uu[e/(e-1),oo) Q. The range of g contains 2. (0, 1) R. The domain of f contains 3. [1/2,1/2] S. The domain of g is 4. (-oo,0)uu(0, oo) 5. (-oo, e/(e-1)] 6. (-oo,0)uu(1/2, e/(e-1)] The correct option is: Prarr4; rarr2; Rrarr1;Srarr1 (b) Prarr3; Qrarr3; Rrarr6; Srarr5 (c) Prarr4; Qrarr2; Rrarr1; Srarr6 (d) Prarr4; Qrarr3; Rrarr6; Srarr5