Q)Solve square root of 3 cos theta space minus space 3 sin theta space equals space 4 sin 2 theta cos 3 theta.

Asked by araima2001 | 1st Mar, 2017, 06:35: AM

Expert Answer:

begin mathsize 16px style square root of 3 space cosθ space minus space 3 space sinθ space space equals space 4 space sin 2 straight theta space space cos 3 straight theta space
rightwards double arrow fraction numerator square root of 3 over denominator 2 end fraction cosθ space minus 3 over 2 space sinθ space space equals space 2 space sin 2 straight theta space space cos 3 straight theta
rightwards double arrow square root of 3 open square brackets 1 half cosθ space minus fraction numerator square root of 3 over denominator 2 end fraction space sinθ close square brackets equals space 2 space sin 2 straight theta space space cos 3 straight theta
rightwards double arrow square root of 3 open square brackets cos open parentheses straight pi over 3 close parentheses cosθ space minus sin open parentheses straight pi over 3 close parentheses space sinθ close square brackets space equals space 2 space sin 2 straight theta space space cos 3 straight theta
rightwards double arrow square root of 3 open square brackets cos open parentheses straight pi over 3 plus straight theta close parentheses close square brackets equals space 2 space sin 2 straight theta space space cos 3 straight theta
rightwards double arrow 2 space sin 2 straight theta space equals space square root of 3 space space and space space cos open parentheses straight pi over 3 plus straight theta close parentheses equals cos 3 straight theta
rightwards double arrow sin 2 straight theta equals fraction numerator space square root of 3 space over denominator 2 end fraction space and space cos open parentheses straight pi over 3 plus straight theta close parentheses equals cos 3 straight theta
rightwards double arrow 2 straight theta equals straight pi over 3 space and space straight pi over 3 plus straight theta equals 3 straight theta
rightwards double arrow straight theta equals straight pi over 6 space and space straight pi over 3 equals 2 straight theta
rightwards double arrow straight theta equals straight pi over 6 space and space straight pi over 6 equals straight theta
end style

Answered by Rebecca Fernandes | 3rd Mar, 2017, 09:44: PM