1
AIEEE 2003
MCQ (Single Correct Answer)
+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
$$\left| a \right| \le {1 \over {\sqrt 2 }}$$
2
AIEEE 2002
MCQ (Single Correct Answer)
+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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