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In triangle ABC, right angled at …

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In triangle ABC, right angled at B, if tanA=1/root3, find the value of : (i) sinA cosC + cosA sinC (ii)cosA cosC – sinA sinC

Posted by Adwaith Sunil 2 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Shreya Gupta 2 years, 1 month ago

Given TanA=1/√3=P/B H^2=P^2+B^2 H^2=(1)^2+(√3)^2 H^2=1+3 H=√4 H=2 Then, SinA=P/H=BC/AC=1/2 SinC=P/H=AB/AC=√3/2 CosA=B/H=AB/AC=√3/2 CosC=B/H=BC/AC=1/2 Hence, (i)sinA cosC + cosA sinC =1/2 × 1/2 + √3/2 × √3/2 =1/4 + 3/4 =4/4 =1 answer Hence, (ii)cosA cosC – sinA sinC =√3/2 × 1/2 - 1/2 × √3/2 =√3/4-√3/4 =0 answer

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