Example no 14 Ch 3 ncert
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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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