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Example no 14 Ch 3 ncert |
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Answer» 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\xa0{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\xa0{tex}cos^2x{/tex}\xa0we get,{tex}cos 2x = 1-tan^2x/1+tan^2x{/tex}Hence Verified. Gud one |
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