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1

IIT-JEE 1997

Fill in the Blanks
The real roots of the equation $$\,{\cos ^7}x + {\sin ^4}x = 1$$ in the interval $$\left( { - \pi ,\pi } \right)$$ are ...., ...., and ______.

Answer

$$ - {\pi \over 2},{\pi \over 2},0$$
2

IIT-JEE 1996

Fill in the Blanks
General value of $$\theta $$ satisfying the equation $${\tan ^2}\theta + \sec \,2\,\theta = 1$$ is _________.

Answer

$$n\pi ,n\pi \pm {\pi \over 3}$$
3

IIT-JEE 1993

Fill in the Blanks
If $$A > 0,B > 0\,$$ and $$A + B = \pi /3,$$ then the maximum value of tan A tan B is _______.

Answer

$${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}$$
4

IIT-JEE 1993

Fill in the Blanks
If $$K = \sin \left( {\pi /18} \right)\sin \left( {5\pi /18} \right)\sin \left( {7\pi /18} \right),$$ then the numerical value of K is ______.

Answer

$${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 8$}}$$

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