1
AIEEE 2007
+4
-1
If sin-1$$\left( {{x \over 5}} \right)$$ + cosec-1$$\left( {{5 \over 4}} \right)$$ = $${\pi \over 2}$$, then the value of x is :
A
4
B
5
C
1
D
3
2
AIEEE 2005
+4
-1
If $${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha ,$$ then $$4{x^2} - 4xy\cos \alpha + {y^2}$$ is equal to :
A
$$2\sin 2\alpha$$
B
$$4$$
C
$$4{\sin ^2}\alpha$$
D
$$-4{\sin ^2}\alpha$$
3
AIEEE 2003
+4
-1
The trigonometric equation $${\sin ^{ - 1}}x = 2{\sin ^{ - 1}}a$$ has a solution for :
A
$$\left| a \right| \ge {1 \over {\sqrt 2 }}$$
B
$${1 \over 2} < \left| a \right| < {1 \over {\sqrt 2 }}$$
C
all real values of $$a$$
D
$$\left| a \right| \le {1 \over {\sqrt 2 }}$$
4
AIEEE 2002
+4
-1
$${\cot ^{ - 1}}\left( {\sqrt {\cos \alpha } } \right) - {\tan ^{ - 1}}\left( {\sqrt {\cos \alpha } } \right) = x,$$ then sin x is equal to :
A
$${\tan ^2}\left( {{\alpha \over 2}} \right)$$
B
$${\cot ^2}\left( {{\alpha \over 2}} \right)$$
C
$$\tan \alpha$$
D
$$cot\left( {{\alpha \over 2}} \right)$$
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