Question

Which of the following is the perfect relation between $\sin \theta$ and $\cos \theta$ for any value of $\theta$?

• A. ${\sin }^2\theta -{\cos }^2\theta =1$
• B. ${\sin }^2\theta +1={\cos }^2\theta$
• C. ${\cos }^2\theta +1={\sin }^2\theta$
• D. $1-{\sin }^2\theta ={\cos }^2\theta$

Answer 1

The correct option is D

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

The relation between $\sin \theta$ and $\cos \theta$ is given by

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

From the above equation, we get

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