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If tantita- ?5\2 then value of cos tita is
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Asked by razaqasmi87 | 29 Jun, 2022, 21:36: PM
answered-by-expert Expert Answer
begin mathsize 14px style tan theta space equals space fraction numerator sin theta over denominator cos theta end fraction space equals fraction numerator square root of 1 minus cos squared theta end root over denominator cos theta end fraction space equals fraction numerator square root of 5 over denominator 2 end fraction end style
By squaring both sides of last two expressions in above mathematical statement,
we get
 
begin mathsize 14px style fraction numerator 1 minus cos squared theta over denominator cos squared theta end fraction space equals 5 over 4 end style
let x = cosθ , then we have begin mathsize 14px style fraction numerator 1 minus x squared over denominator x squared end fraction space equals space 5 over 4 end style
By solving above equation, we get x = cosθ = 2/3
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Alternate method
 
Let us consider a triangle ABC such that begin mathsize 14px style angle end styleA = 90o , begin mathsize 14px style angle end styleB = θ ,
side AC = √5 units and AB = 2 units , so that tanθ = √5 / 2
 
Side BC can be calculated as 3 unitsas given below
 
begin mathsize 14px style B C space equals space square root of A C squared plus A B squared end root space equals square root of 5 plus 4 end root space equals space 3 space u n i t s end style
 
Then cosθ = 2/3
Answered by Thiyagarajan K | 30 Jun, 2022, 00:26: AM
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