Question

Evaluate $1–2\sin \theta \cos \theta$ if $\sin \theta =\cos \theta$.

• A. 1
• B. - 1
• C. 0
• D. 2

Answer 1

The correct option is C

0

We can write $1$ as ${\sin }^2\theta +{\cos }^2\theta$

Therefore, $1-2\sin \theta \cos \theta ={\sin }^2\theta +{\cos }^2\theta -2\sin \theta \cos \theta$

$=(\sin \theta -\cos \theta {)}^2$

If $\sin \theta =\cos \theta ,$ then $(\sin \theta -\cos \theta {)}^2=0$