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ICSE Class 9 Answered

If Tan theta is root2 -1, then prove that sin theta.cos theta = 1/2 root 2  
Asked by prashanth.rajappa | 16 Dec, 2018, 23:16: PM
answered-by-expert Expert Answer
As shown in figure, if tanθ = √2-1, then sinθ = (√2-1) / BC  and cosθ = 1/BC
 
Hence sinθ × cosθ = begin mathsize 12px style fraction numerator square root of 2 space minus space 1 over denominator B C squared end fraction space equals space fraction numerator square root of 2 space minus space 1 over denominator begin display style open parentheses square root of 2 space minus space 1 close parentheses squared end style begin display style plus end style begin display style 1 end style end fraction space equals space fraction numerator square root of 2 space minus space 1 over denominator 4 minus 2 square root of 2 end fraction space equals fraction numerator square root of 2 space minus space 1 over denominator 2 square root of 2 open parentheses square root of 2 space minus space 1 close parentheses end fraction space equals space fraction numerator 1 over denominator 2 square root of 2 end fraction end style 
Answered by Thiyagarajan K | 17 Dec, 2018, 10:26: AM

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