Question

Which of the following is/are FALSE $\forall \theta \in R$?

• A. $\sin \theta =1-\cos \theta$
• B. $\sec \theta -\tan \theta =\frac{1}{\sec \theta +\tan \theta }$
• C. ${\tan }^2\theta -{\sin }^2\theta ={\tan }^2\theta {\sin }^2\theta$
• D. $\sin \frac{\pi }{3}=\cos \frac{\pi }{6}$

Answer 1

Answer: (A)

$\sin \theta =1-\cos \theta$

Dividing LHS by RHS we get,

in $A\to \frac{sin\theta }{1-cos\theta }\ne 1$

in $B\to se{c}^2\theta -ta{n}^2\theta =1$

in $C\to cose{c}^2\theta -co{t}^2\theta =1$

in $D\to \frac{\frac{\sqrt{3}}{2}}{\frac{\sqrt{3}}{2}}=1$

Therefore, Answer is $sin\theta =1-cos\theta$