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CBSE Class 12-science Answered

sin[2cos^-1✓5/3] Is equal to
Asked by YOGESH VENKATESWARAN | 23 Apr, 2019, 09:21: PM
answered-by-expert Expert Answer
T o space f i n d colon space sin open square brackets 2 cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 5 over denominator 3 end fraction close parentheses close square brackets L e t space x equals 2 cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 5 over denominator 3 end fraction close parentheses rightwards double arrow x over 2 equals cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 5 over denominator 3 end fraction close parentheses rightwards double arrow cos open parentheses x over 2 close parentheses equals fraction numerator square root of 5 over denominator 3 end fraction space........... space left parenthesis i right parenthesis W e space k n o w space t h a t space 2 cos squared x minus 1 equals cos 2 x space rightwards double arrow space cos x equals square root of fraction numerator 1 plus cos 2 x over denominator 2 end fraction end root A p p l y i n g space t h i s space i n space left parenthesis i right parenthesis comma space w e space h a v e square root of fraction numerator 1 plus cos x over denominator 2 end fraction end root equals fraction numerator square root of 5 over denominator 3 end fraction rightwards double arrow fraction numerator 1 plus cos x over denominator 2 end fraction equals 5 over 9 rightwards double arrow 1 plus cos x equals 10 over 9 rightwards double arrow cos x equals 1 over 9 space.... space left parenthesis i i right parenthesis W e space k n o w space t h a t space sin squared x plus cos squared equals 1 rightwards double arrow sin x equals square root of 1 minus cos squared x end root U sin g space left parenthesis i i right parenthesis space i n space t h e space a b o v e space e q u a l i t y comma space w e space h a v e sin x equals square root of 1 minus open parentheses 1 over 9 close parentheses squared end root rightwards double arrow sin x equals square root of 1 minus 1 over 81 end root rightwards double arrow sin x equals square root of 80 over 81 end root rightwards double arrow x equals sin to the power of negative 1 end exponent open parentheses square root of 80 over 81 end root close parentheses T h u s comma space w e space h a v e sin open square brackets 2 cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 5 over denominator 3 end fraction close parentheses close square brackets equals sin x equals sin open parentheses sin to the power of negative 1 end exponent open parentheses square root of 80 over 81 end root close parentheses close parentheses equals square root of 80 over 81 end root equals fraction numerator 4 square root of 5 over denominator 9 end fraction H e n c e comma space sin open square brackets 2 cos to the power of negative 1 end exponent open parentheses fraction numerator square root of 5 over denominator 3 end fraction close parentheses close square brackets equals fraction numerator 4 square root of 5 over denominator 9 end fraction
Answered by Renu Varma | 24 Apr, 2019, 10:25: AM

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