If cosectheta – sin theta= a and sec theta  – cos theta = b, then find the value of (a2b)2/3 + (ab2 ) 2/3 . (A) 0 (B) –1 (C) 2 (D) 1 (E) None of these
 
this is olympais question .. solve the with short time and tell me the process with steps proper .

Asked by sucharitasahoo1 | 30th Nov, 2017, 09:06: PM

Expert Answer:

begin mathsize 16px style cosec space straight theta minus sin space straight theta equals straight a
rightwards double arrow fraction numerator 1 over denominator sin space straight theta end fraction minus sin space straight theta equals straight a
rightwards double arrow fraction numerator 1 minus sin squared space straight theta over denominator sin space straight theta end fraction equals straight a
rightwards double arrow fraction numerator cos squared space straight theta over denominator sin space straight theta end fraction equals straight a
sec space straight theta minus cos space straight theta equals straight b
rightwards double arrow fraction numerator 1 over denominator cos space straight theta end fraction minus cos space straight theta equals straight b
rightwards double arrow fraction numerator 1 minus cos squared space straight theta over denominator cos space straight theta end fraction equals straight b
rightwards double arrow fraction numerator sin squared space straight theta over denominator cos space straight theta end fraction equals straight b
Now comma
open parentheses straight a squared straight b close parentheses to the power of 2 over 3 end exponent plus open parentheses ab squared close parentheses to the power of 2 over 3 end exponent
equals open parentheses fraction numerator cos to the power of 4 space straight theta over denominator sin squared space straight theta end fraction cross times fraction numerator sin squared space straight theta over denominator cos space straight theta end fraction close parentheses to the power of 2 over 3 end exponent plus open parentheses fraction numerator cos squared space straight theta over denominator sin space straight theta end fraction cross times fraction numerator sin to the power of 4 space straight theta over denominator cos squared space straight theta end fraction close parentheses to the power of 2 over 3 end exponent
equals open parentheses cos cubed space straight theta close parentheses to the power of 2 over 3 end exponent plus open parentheses sin cubed space straight theta close parentheses to the power of 2 over 3 end exponent
equals cos squared space straight theta plus sin squared space straight theta
equals 1 end style

Answered by Rashmi Khot | 1st Dec, 2017, 08:55: AM