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Kritika Trehan 8 years, 1 month ago
Binomial theorem is heavily used in probability theory . Binomial theorem is used in forecast services .the future weather forecasting is impossible without binomial theorem.the disaster forecast is also depend upon binomial theorems
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Shoba Ponnuraj 8 years, 1 month ago
Example 14: {tex}cos 2x = cos^2x – sin^2 x = 2 cos^2 x – 1 = 1 – 2 sin^2 x = 1-tan^2x/1+tan^2x{/tex}
solution :
we know that {tex} cos (x + y) = cos x cos y – sin x sin y{/tex}
Replacing y by x, we get
{tex}cos 2x = cos^2x – sin^2 x = 2 cos^2 x – 1 {/tex}
{tex}= cos^2 x – (1 – cos^2 x) = 2 cos^2x – 1{/tex}
Again,
{tex}cos 2x = cos^2 x – sin^2 x{/tex}
{tex}= 1 – sin^2 x – sin^2 x = 1 – 2 sin^2 x.{/tex}
we have,
{tex} cos 2x = cos^2 x – sin ^2 x =(cos^2 x – sin ^2 x) /( cos^2 x +sin ^2 x){/tex}
Dividing each term by {tex}cos^2x{/tex} we get,
{tex}cos 2x = 1-tan^2x/1+tan^2x{/tex}
Hence Verified.
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A relation is a function if it "maps" elements of one set to another set. That means that each element in the first set can appear at most in one pair in the first entry.
The example shows two elements of the first set can be mapped to the same element of the second set.
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