Question

Prove the following identity sin x(sec x+cscx)= tan x +1

Answer 1

Answer:

Step-by-step explanation:

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FACTS TO KNOW BEFORE SOLVING :-

• $\sin x = \frac{1}{cosec \: x} \: \: or \: \: cosex \: x = \frac{1}{\sin x}$

• $\cos x = \frac{1}{\sec x} \: \:or \: \: \sec x = \frac{1}{\cos x}$

• $\tan x = \frac{\sin x}{\cos x}$

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In the question ,

L.H.S. = $\sin x (\sec x + cosec \: x)$

R.H.S. = $\tan x + 1$

Lets solve L.H.S. first.

$\sin x (\sec x + cosec \: x)$

$=> \sin x( \frac{1}{\cos x} + \frac{1}{\sin x} )$

$=> \frac{\sin x}{\cos x} + \frac{\sin x}{\sin x}$

$=> \tan x + 1$

∴ L.H.S. = R.H.S. (Proved)