CBSE Class 10 Answered
If tan^2A=1-a^2, prove that secA+tan^3cosecA=(2-a^2)^3/2
please answer in a simple way.
Asked by guptaabhinav0809 | 10 Feb, 2019, 23:44: PM
tan2A = 1 - a2
LHS
= sec A + tan3 A cosec A
= ![begin mathsize 16px style square root of 1 plus tan squared straight A end root plus tan squared straight A cross times tanA square root of 1 plus cot squared straight A end root space space space space because 1 plus tan squared straight A equals sec squared straight A space and space cosec squared straight A minus cot squared straight A equals 1
end style](https://images.topperlearning.com/topper/tinymce/cache/19fcbf8522be5116fc3b9b785166eaad.png)
![begin mathsize 16px style square root of 1 plus tan squared straight A end root plus tan squared straight A cross times tanA square root of 1 plus cot squared straight A end root space space space space because 1 plus tan squared straight A equals sec squared straight A space and space cosec squared straight A minus cot squared straight A equals 1
end style](https://images.topperlearning.com/topper/tinymce/cache/19fcbf8522be5116fc3b9b785166eaad.png)
= ![begin mathsize 16px style square root of 1 plus open parentheses 1 minus straight a squared close parentheses end root plus open parentheses 1 minus straight a squared close parentheses square root of open parentheses 1 minus straight a squared close parentheses end root cross times square root of 1 plus fraction numerator 1 over denominator tan squared straight A end fraction end root end style](https://images.topperlearning.com/topper/tinymce/cache/5598a40f7fad285859a57cce9d9a3e78.png)
![begin mathsize 16px style square root of 1 plus open parentheses 1 minus straight a squared close parentheses end root plus open parentheses 1 minus straight a squared close parentheses square root of open parentheses 1 minus straight a squared close parentheses end root cross times square root of 1 plus fraction numerator 1 over denominator tan squared straight A end fraction end root end style](https://images.topperlearning.com/topper/tinymce/cache/5598a40f7fad285859a57cce9d9a3e78.png)
= ![begin mathsize 16px style square root of 2 minus straight a squared end root plus open parentheses 1 minus straight a squared close parentheses square root of open parentheses 1 minus straight a squared close parentheses end root cross times square root of 1 plus fraction numerator 1 over denominator 1 minus straight a squared end fraction end root end style](https://images.topperlearning.com/topper/tinymce/cache/1eae4fd3332b478325163efeb5b85101.png)
![begin mathsize 16px style square root of 2 minus straight a squared end root plus open parentheses 1 minus straight a squared close parentheses square root of open parentheses 1 minus straight a squared close parentheses end root cross times square root of 1 plus fraction numerator 1 over denominator 1 minus straight a squared end fraction end root end style](https://images.topperlearning.com/topper/tinymce/cache/1eae4fd3332b478325163efeb5b85101.png)
= ![Error converting from MathML to accessible text.](https://images.topperlearning.com/topper/tinymce/cache/f3526c87c8ef1561be42ab796f3704c1.png)
![Error converting from MathML to accessible text.](https://images.topperlearning.com/topper/tinymce/cache/f3526c87c8ef1561be42ab796f3704c1.png)
= ![begin mathsize 16px style square root of 2 minus straight a squared end root plus open parentheses 1 minus straight a squared close parentheses cross times square root of 2 minus straight a squared end root end style](https://images.topperlearning.com/topper/tinymce/cache/cf2683d22f8c6b5515a240f3763eb080.png)
![begin mathsize 16px style square root of 2 minus straight a squared end root plus open parentheses 1 minus straight a squared close parentheses cross times square root of 2 minus straight a squared end root end style](https://images.topperlearning.com/topper/tinymce/cache/cf2683d22f8c6b5515a240f3763eb080.png)
= ![Error converting from MathML to accessible text.](https://images.topperlearning.com/topper/tinymce/cache/1f9dd409f8f0bbb95f63a7abc3e4b708.png)
![Error converting from MathML to accessible text.](https://images.topperlearning.com/topper/tinymce/cache/1f9dd409f8f0bbb95f63a7abc3e4b708.png)
= ![Error converting from MathML to accessible text.](https://images.topperlearning.com/topper/tinymce/cache/238c0e86febbf09994e590819731150e.png)
![Error converting from MathML to accessible text.](https://images.topperlearning.com/topper/tinymce/cache/238c0e86febbf09994e590819731150e.png)
Answered by Sneha shidid | 11 Feb, 2019, 09:59: AM
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