Trigonometric Identities Question 233
Question: The value of $ {{\tan }^{2}}\theta {{\sec }^{2}}\theta ({{\cot }^{2}}\theta -{{\cos }^{2}}\theta ) $ is
Options:
A) $ 0 $
B) $ 1 $
C) $ -1 $
D) $ \frac{1}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ {{\tan }^{2}}\theta sec^{2}\theta ({{\cot }^{2}}\theta -{{\cos }^{2}}\theta ) $ $ ={{\sec }^{2}}\theta ({{\tan }^{2}}\theta {{\cot }^{2}}\theta -{{\tan }^{2}}\theta {{\cos }^{2}}\theta ) $ $ ={{\sec }^{2}}\theta ( 1-\frac{{{\sin }^{2}}\theta }{{{\cos }^{2}}\theta }{{\cos }^{2}}\theta )={{\sec }^{2}}\theta (1-{{\sin }^{2}}\theta ) $ $ ={{\sec }^{2}}\theta .,{{\cos }^{2}}\theta =1 $
BETA
