Question

1 - sin theta is equal to

Answer 1

Step-by-step explanation:

cos theta . 1-sin^2 theta = cos^2 theta.. taking square root cos theta =1-sintheta

Answer 2

The value of $1 - \sin \theta$ is equal to$(\sin \dfrac{A}{2} -\cos \dfrac{A}{2})^2.$

Step-by-step explanation:

We have,

$1 - \sin \theta$

To find, the value of $1 - \sin \theta$ = ?

∴ $1 - \sin \theta$               ......... (1)

Using the trigonometric identity,

$\sin^2 \dfrac{A}{2} +\cos^2 \dfrac{A}{2}=1$ and

$\sin A=2\sin \dfrac{A}{2}\cos \dfrac{A}{2}$

Now, equation (1) can be written as,

$=\sin^2 \dfrac{A}{2} +\cos^2 \dfrac{A}{2}-2\sin \dfrac{A}{2}\cos \dfrac{A}{2}$

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

∴ The value of $1 - \sin \theta$ $=(\sin \dfrac{A}{2} -\cos \dfrac{A}{2})^2$

Thus, the value of $1 - \sin \theta$ is equal to$(\sin \dfrac{A}{2} -\cos \dfrac{A}{2})^2.$