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CBSE Class 10 Answered

Please prove A = B.
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Asked by malaysaha.80 | 23 Feb, 2019, 10:20: PM
answered-by-expert Expert Answer
begin mathsize 12px style fraction numerator sin to the power of 4 A over denominator cos squared B end fraction plus fraction numerator begin display style cos to the power of 4 A end style over denominator begin display style sin squared B end style end fraction space equals space 1
sin to the power of 4 A space sin squared B space plus space cos to the power of 4 A space cos squared B space equals space sin squared B space cos squared B
sin to the power of 4 A space sin squared B space plus space left square bracket space 1 space minus space sin squared A right square bracket squared space left square bracket 1 space minus space sin squared B right square bracket space equals space sin squared B space left square bracket 1 space minus space sin squared B right square bracket
sin to the power of 4 A space sin squared B space plus left square bracket space 1 space plus space sin to the power of 4 A space minus space 2 space sin squared A space right square bracket space left square bracket space 1 space minus space sin squared B space right square bracket space equals space sin squared B space minus space sin to the power of 4 B
sin to the power of 4 A space sin squared B space plus 1 space plus space sin to the power of 4 A space minus space 2 space sin squared A space minus sin squared B space minus sin to the power of 4 A space sin squared B space plus 2 sin squared A sin squared B space equals space sin squared B space minus space sin to the power of 4 B
1 plus space sin to the power of 4 A space plus sin to the power of 4 B plus space 2 sin squared A space sin squared B space minus 2 left parenthesis space sin squared A space plus sin squared B right parenthesis space equals space 0
1 plus space left parenthesis space sin squared A space plus sin squared B right parenthesis squared space minus space 2 left parenthesis space sin squared A space plus sin squared B right parenthesis space equals space 0
left parenthesis space sin squared A space plus sin squared B space minus space 1 right parenthesis squared space equals 0 space space space space space space o r space space space sin squared A space equals space left parenthesis space 1 space minus space sin squared B right parenthesis space space equals space cos squared B space space space space
space o r space space sin space A space equals space cos space B space equals space sin left parenthesis 90 minus space B right parenthesis
H e n c e space A space equals space 90 minus B end style
 
I checked the validity of the given trigonometric equation in EXCEL. This equation is valid only if A and B are complimentary angles.
(sum of A and B is 90°)
This equation is valid for A=B only if A=B=45°. If other equal value is substituted for A and B, Equation is not valid
Answered by Thiyagarajan K | 24 Feb, 2019, 12:05: AM
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