if sin 1x sin 1y pi 2 then 1 x 4 y 4x 2 x 2y 2 y 2 is equal

If $${\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{\pi }{2},$$ then $$\frac{{1 + {x^4} + {y^4}}}{{{x^2} - {x^2}{y^2} + {y^2}}}\,$$ is equal to

A. $$1$$

B. $$2$$

C. $$\frac{1}{2}$$

D. None of these

Answer : $$2$$

Solution :
$$\eqalign{ & {\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{\pi }{2} \cr & \Rightarrow {\sin ^{ - 1}}x = \frac{\pi }{2} - {\sin ^{ - 1}}y \cr & \Rightarrow {\sin ^{ - 1}}x = {\sin ^{ - 1}}\sqrt {1 - {y^2}} \cr & \Rightarrow {x^2} + {y^2} = 1 \cr & \Rightarrow \frac{{1 + {x^4} + {y^4}}}{{{x^2} - {x^2}{y^2} + {y^2}}} = \frac{{1 + {{\left( {{x^2} + {y^2}} \right)}^2} - 2{x^2}{y^2}}}{{1 - {x^2}{y^2}}} \cr & = \frac{{1 + 1 - 2{x^2}{y^2}}}{{1 - {x^2}{y^2}}} = 2. \cr} $$

Releted MCQ Question on
Trigonometry >> Inverse Trigonometry Function

Releted Question 1

The value of $$\tan \left[ {{{\cos }^{ - 1}}\left( {\frac{4}{5}} \right) + {{\tan }^{ - 1}}\left( {\frac{2}{3}} \right)} \right]$$ is

A. $$\frac{6}{{17}}$$

B. $$\frac{7}{{16}}$$

C. $$\frac{16}{{7}}$$

D. none

View Answer

Releted Question 2

If we consider only the principle values of the inverse trigonometric functions then the value of $$\tan \left( {{{\cos }^{ - 1}}\frac{1}{{5\sqrt 2 }} - {{\sin }^{ - 1}}\frac{4}{{\sqrt {17} }}} \right)$$ is

A. $$\frac{{\sqrt {29} }}{3}$$

B. $$\frac{{29}}{3}$$

C. $$\frac{{\sqrt {3}}}{29}$$

D. $$\frac{{3}}{29}$$

View Answer

Releted Question 3

The number of real solutions of $${\tan ^{ - 1}}\sqrt {x\left( {x + 1} \right)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = \frac{\pi }{2}$$ is

A. zero

B. one

C. two

D. infinite

View Answer

Releted Question 4

If $${\sin ^{ - 1}}\left( {x - \frac{{{x^2}}}{2} + \frac{{{x^3}}}{4} - .....} \right) + {\cos ^{ - 1}}\left( {{x^2} - \frac{{{x^4}}}{2} + \frac{{{x^6}}}{4} - .....} \right) = \frac{\pi }{2}$$ for $$0 < \left| x \right| < \sqrt 2 ,$$ then $$x$$ equals

A. $$ \frac{1}{2}$$

B. 1

C. $$ - \frac{1}{2}$$

D. $$- 1$$

View Answer

If $${\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{\pi }{2},$$ then $$\frac{{1 + {x^4} + {y^4}}}{{{x^2} - {x^2}{y^2} + {y^2}}}\,$$ is equal to

Releted MCQ Question on
Trigonometry >> Inverse Trigonometry Function

The value of $$\tan \left[ {{{\cos }^{ - 1}}\left( {\frac{4}{5}} \right) + {{\tan }^{ - 1}}\left( {\frac{2}{3}} \right)} \right]$$ is

If we consider only the principle values of the inverse trigonometric functions then the value of $$\tan \left( {{{\cos }^{ - 1}}\frac{1}{{5\sqrt 2 }} - {{\sin }^{ - 1}}\frac{4}{{\sqrt {17} }}} \right)$$ is

The number of real solutions of $${\tan ^{ - 1}}\sqrt {x\left( {x + 1} \right)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = \frac{\pi }{2}$$ is

If $${\sin ^{ - 1}}\left( {x - \frac{{{x^2}}}{2} + \frac{{{x^3}}}{4} - .....} \right) + {\cos ^{ - 1}}\left( {{x^2} - \frac{{{x^4}}}{2} + \frac{{{x^6}}}{4} - .....} \right) = \frac{\pi }{2}$$ for $$0 < \left| x \right| < \sqrt 2 ,$$ then $$x$$ equals

Practice More Releted MCQ Question on
Inverse Trigonometry Function

Practice More MCQ Question on Maths Section

If $${\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{\pi }{2},$$ then $$\frac{{1 + {x^4} + {y^4}}}{{{x^2} - {x^2}{y^2} + {y^2}}}\,$$ is equal to

Releted MCQ Question on Trigonometry >> Inverse Trigonometry Function

The value of $$\tan \left[ {{{\cos }^{ - 1}}\left( {\frac{4}{5}} \right) + {{\tan }^{ - 1}}\left( {\frac{2}{3}} \right)} \right]$$ is

If we consider only the principle values of the inverse trigonometric functions then the value of $$\tan \left( {{{\cos }^{ - 1}}\frac{1}{{5\sqrt 2 }} - {{\sin }^{ - 1}}\frac{4}{{\sqrt {17} }}} \right)$$ is

The number of real solutions of $${\tan ^{ - 1}}\sqrt {x\left( {x + 1} \right)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = \frac{\pi }{2}$$ is

If $${\sin ^{ - 1}}\left( {x - \frac{{{x^2}}}{2} + \frac{{{x^3}}}{4} - .....} \right) + {\cos ^{ - 1}}\left( {{x^2} - \frac{{{x^4}}}{2} + \frac{{{x^6}}}{4} - .....} \right) = \frac{\pi }{2}$$ for $$0 < \left| x \right| < \sqrt 2 ,$$ then $$x$$ equals

Practice More Releted MCQ Question on Inverse Trigonometry Function

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Trigonometry >> Inverse Trigonometry Function

Practice More Releted MCQ Question on
Inverse Trigonometry Function