1. cos^-1(a) + cos^-1(b) + cos^-1(c) = 3pi then find value of a(b+c) + b(c+a) + c(a+b)
 
2. write the number of real solutions of the equation (1+cos2x)^1/2 = 2^1/2 cos^-1(cosx) in [pi/2, pi]
 
3. sin^-1(x) + sin^-1(1-x) = cot^-1(x)
 


 

Asked by sugatac | 7th Jun, 2015, 09:42: PM

Expert Answer:

1. space W e space k n o w comma space cos to the power of negative 1 end exponent x space h a s space t h e space r a n g e space o f space open square brackets 0 comma space straight pi close square brackets space  S i n c e space cos to the power of negative 1 end exponent a plus cos to the power of negative 1 end exponent b plus cos to the power of negative 1 end exponent c equals 3 straight pi therefore cos to the power of negative 1 end exponent a equals cos to the power of negative 1 end exponent b equals cos to the power of negative 1 end exponent c equals straight pi therefore straight a equals b equals c equals cos space straight pi equals negative 1  straight a left parenthesis straight b plus straight c right parenthesis plus straight b left parenthesis straight c plus straight a right parenthesis plus straight c left parenthesis straight a plus straight b right parenthesis equals negative 1 open parentheses negative 1 minus 1 close parentheses minus 1 open parentheses negative 1 minus 1 close parentheses minus 1 open parentheses negative 1 minus 1 close parentheses equals 2 plus 2 plus 2 equals 6 P l e a s e space p o s t space e a c h space q u e s t i o n space s e p a r a t e l y.

Answered by Prasenjit Paul | 8th Jun, 2015, 11:12: AM

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