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Annette [7]
3 years ago
12

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

Mathematics
1 answer:
Alexxandr [17]3 years ago
3 0

Answer:

Step-by-step explanation:

<u>________________________________________________________</u>

<u>FACTS TO KNOW BEFORE SOLVING :-</u>

  • <u></u>\sin x = \frac{1}{cosec \: x} \: \: or \: \: cosex \: x = \frac{1}{\sin x}<u></u>
  • <u></u>\cos x = \frac{1}{\sec x}  \: \:or \: \: \sec x = \frac{1}{\cos x}<u></u>
  • <u></u>\tan x = \frac{\sin x}{\cos x}<u></u>

<u>________________________________________________________</u>

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)

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<u><em>Domain:</em></u>

The domain is all real numbers except where the slope is undefined (a vertical line). In this case, no number makes the expression undefined, so the domain is:

all real numbers

<u><em>Interval notation:</em></u><em>  </em>(-∞,∞)

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<em><u>Set-Builder Notation:</u></em> {x | x ∈ R }

<em><u>Range:</u></em>

The range is the set of all valid values. Graph the line and check. Since all values of y are valid, the range is:

all real numbers

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:Done

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