Question

show that one by cos theta minus cos theta equals to tan theta × sin theta​

Answer 1

Step-by-step explanation:

see the answer solved in Image Uploaded

Answer 2

$\dfrac{1}{\cos \theta} -\cos \theta=\tan \theta \times \sin \theta​$, shown.

Step-by-step explanation:

Show that $\dfrac{1}{\cos \theta} -\cos \theta=\tan \theta \times \sin \theta​$.

L.H.S. $=\dfrac{1}{\cos \theta} -\cos \theta$

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

Using the trigonometric identity,

$\sin^2 A+\cos^2 A=1$

⇒ $\sin^2 A=1-\cos^2 A$

$=\dfrac{\sin^2 \theta}{\cos \theta}$

$=\dfrac{\sin \theta}{\cos \theta}\times\sin \theta$

Using the trigonometric identity,

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

$=\tan \theta\times\sin \theta$

= R.H.S., shown.

∴$\dfrac{1}{\cos \theta} -\cos \theta=\tan \theta \times \sin \theta​$, shown.