1. what is the anxwer of sin^-1{sinx +cosx/square root of 2}
  2.                                 cos^-1{cosx +sinx/ square root of 2}                

Asked by Sagar krishna | 21st Jun, 2014, 10:48: AM

Expert Answer:

1. space C o n s i d e r space t h e space g i v e n space e x p r e s s i o n : sin to the power of minus 1 end exponent open curly brackets fraction numerator sin x plus cos x over denominator square root of 2 end fraction close curly brackets sin to the power of minus 1 end exponent open curly brackets fraction numerator sin x plus cos x over denominator square root of 2 end fraction close curly brackets equals sin to the power of minus 1 end exponent open curly brackets fraction numerator sin x over denominator square root of 2 end fraction plus fraction numerator cos x over denominator square root of 2 end fraction close curly brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals sin to the power of minus 1 end exponent open curly brackets sin x cross times cos straight pi over 4 plus cos x cross times sin straight pi over 4 close curly brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals sin to the power of minus 1 end exponent open curly brackets sin open parentheses x plus straight pi over 4 close parentheses close curly brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals x plus straight pi over 4 2. space C o n s i d e r space t h e space g i v e n space e x p r e s s i o n : cos to the power of minus 1 end exponent open curly brackets fraction numerator sin x plus cos x over denominator square root of 2 end fraction close curly brackets cos to the power of minus 1 end exponent open curly brackets fraction numerator sin x plus cos x over denominator square root of 2 end fraction close curly brackets equals cos to the power of minus 1 end exponent open curly brackets fraction numerator sin x over denominator square root of 2 end fraction plus fraction numerator cos x over denominator square root of 2 end fraction close curly brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals c os to the power of minus 1 end exponent open curly brackets cos x cross times cos straight pi over 4 plus sin x cross times sin straight pi over 4 close curly brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals cos to the power of minus 1 end exponent open curly brackets cos open parentheses x minus straight pi over 4 close parentheses close curly brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals x minus straight pi over 4 space space space space space space space space space space space space space space space space space space space space space space space space space space

Answered by Vimala Ramamurthy | 21st Jun, 2014, 01:18: PM