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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, 11:44: PM
answered-by-expert Expert Answer
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
= 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
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
Error converting from MathML to accessible text.
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
Error converting from MathML to accessible text.
Error converting from MathML to accessible text.
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