PROVE THAT  


Asked by Kusum and Sanjeet | 9th May, 2016, 10:27: AM

Expert Answer:

W e space k n o w space t h a t comma tan to the power of negative 1 end exponent x equals s e c to the power of negative 1 end exponent open parentheses square root of 1 plus x squared end root close parentheses therefore t a n to the power of negative 1 end exponent 2 equals s e c to the power of negative 1 end exponent open parentheses square root of 1 plus 2 squared end root close parentheses equals s e c to the power of negative 1 end exponent square root of 5 S i m i l a r l y comma c o t to the power of negative 1 end exponent x equals c o s e c to the power of negative 1 end exponent open parentheses square root of 1 plus x squared end root close parentheses therefore c o t to the power of negative 1 end exponent 3 equals equals c o s e c to the power of negative 1 end exponent open parentheses square root of 1 plus 3 squared end root close parentheses equals equals c o s e c to the power of negative 1 end exponent open parentheses square root of 10 close parentheses C o n s i d e r space t h e space l e f t space h a n d space s i d e space o f space t h e space g i v e n space e q u a t i o n colon s e c squared open parentheses t a n to the power of negative 1 end exponent open parentheses 2 close parentheses close parentheses plus c o s e c squared open parentheses c o t to the power of negative 1 end exponent open parentheses 3 close parentheses close parentheses equals s e c squared open parentheses s e c to the power of negative 1 end exponent square root of 5 close parentheses plus c o s e c squared open parentheses c o s e c to the power of negative 1 end exponent open parentheses square root of 10 close parentheses close parentheses equals open square brackets s e c open parentheses s e c to the power of negative 1 end exponent square root of 5 close parentheses close square brackets squared plus open square brackets cos e c open parentheses cos e c to the power of negative 1 end exponent open parentheses square root of 10 close parentheses close parentheses close square brackets squared equals open square brackets open parentheses square root of 5 close parentheses squared plus open parentheses square root of 10 close parentheses squared close square brackets equals 5 plus 10 equals 15 equals R H S H e n c e space p r o v e d.

Answered by Vimala | 9th May, 2016, 11:22: AM

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