Inverse Trigonometric Functions Question 100
Question: What is the value of $ {{\sec }^{2}}{{\tan }^{-1}}( \frac{5}{11} )? $
Options:
A) $ 121/96 $
B) $ 211/921 $
C) $ 146/121 $
D) $ 267/121 $
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Answer:
Correct Answer: C
Let $ {{\sec }^{2}}( {{\tan }^{-1}}( \frac{5}{11} ) ) $
$ =1+{{\tan }^{2}}( {{\tan }^{-1}}( \frac{5}{11} ) )( \because {{\sec }^{2}}\theta -{{\tan }^{2}}\theta =1 ) $
$ =1+{{[ \tan ( {{\tan }^{-1}}( \frac{5}{11} ) ) ]}^{2}}=1+{{( \frac{5}{11} )}^{2}} $
$ =1+\frac{25}{121}=\frac{146}{121} $
BETA
