Question

State the whether given statement is true or false

$1-\tan \theta \tan 2\theta =\sec 2\theta$.

• A. True
• B. False

Answer 1

The correct option is B False

$1-\tan \theta \tan 2\theta =1-\frac{\sin \theta \sin 2\theta }{\cos \theta \cos 2\theta }$

putting in form of sin and cos an simplifying

$=\frac{\cos \theta \cos 2\theta -\sin \theta \sin 2\theta }{\cos \theta \cos 2\theta }$

$=\frac{\cos 3\theta }{\frac{1}{2}(\cos 3\theta +\cos \theta )}$ ............... $\cos (a+b)=\cos a\cdot \cos b-\sin a\cdot sinb$ and $\cos C+\cos D$

$=\frac{2\cos 3\theta }{\cos 3\theta +\cos \theta }\ne \sec 2\theta$