IF fraction numerator cos to the power of 4 theta over denominator cos squared ϕ end fraction+fraction numerator sin to the power of 4 theta over denominator sin squared ϕ end fraction=1,then prove that fraction numerator cos to the power of 4 ϕ over denominator cos squared theta end fraction+fraction numerator sin to the power of 4 ϕ over denominator sin squared theta end fraction=1

Asked by abinash.gupta003 | 30th Jul, 2017, 12:22: PM

Expert Answer:

begin mathsize 16px style fraction numerator cos to the power of 4 space theta over denominator cos squared space empty set end fraction plus fraction numerator begin display style sin to the power of 4 space theta end style over denominator begin display style sin squared space empty set end style end fraction equals 1
rightwards double arrow fraction numerator begin display style cos to the power of 4 space theta end style over denominator begin display style cos squared space empty set end style end fraction plus fraction numerator begin display style sin to the power of 4 space theta end style over denominator begin display style sin squared space empty set end style end fraction equals cos squared space empty set plus sin squared space empty set
rightwards double arrow open parentheses cos squared space empty set minus fraction numerator begin display style cos to the power of 4 space theta end style over denominator begin display style cos squared space empty set end style end fraction close parentheses plus open parentheses sin squared space empty set minus fraction numerator begin display style sin to the power of 4 space theta end style over denominator begin display style sin squared space empty set end style end fraction close parentheses equals 0
rightwards double arrow cos to the power of 4 space empty set plus sin to the power of 4 space empty set equals cos to the power of 4 space theta plus sin to the power of 4 space theta
rightwards double arrow sin space ϕ space cos ϕ equals sin theta cos theta
rightwards double arrow sin space open parentheses 2 empty set close parentheses equals sin space left parenthesis 2 theta right parenthesis
You space can space solve space it space further.
This space type space of space questions space are space not space in space Class space straight X thin space syllabus. end style

Answered by Rashmi Khot | 31st Jul, 2017, 10:13: AM