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Class 10 Class 12

ત્રિકોણમિતિ

∆ABCમાં m∠C = 90 અને ten A = $fraction numerator bold 1 over denominator square root of bold 3 end fraction$ , તો sin A અને cos B શોધો.

∆ABCમાં AC = 5, BC = 13, m∠A = 90, તો ∠Bના તમામ ત્રિકોણમિતીઉઅ ગુણોત્તર મેળવો.

જો cosec A = $square root of bold 10$ હોય, તો બાકીના પાંચ ત્રિકોણમિતીય ગુણોત્તર શોધો.

∆ABC માં m∠B = 90 લઈએ.

cosec A = $bold AC over bold AB bold space bold equals bold space fraction numerator square root of bold 10 over denominator bold 1 end fraction$

$bold therefore fraction numerator bold AC over denominator square root of bold 10 end fraction bold space bold equals bold space bold BC over bold 1 bold space bold equals bold space bold k bold space bold left parenthesis bold ધ ા ર ો bold space bold ક ે bold right parenthesis bold space bold જ ્ ય ાં bold space bold k bold space bold greater than bold space bold 0 bold therefore bold space bold AC bold space bold equals bold space square root of bold 10 bold space bold k bold. bold space bold BC bold space bold equals bold space bold k bold space$

હવે, AC² = AB² + BC²

$bold therefore bold space bold left parenthesis square root of bold 10 bold space bold k bold right parenthesis to the power of bold 2$ = AB² + k²

AB = 3k (∵ k>0)

આમ, AC = , BC = $square root of 10$ k અને AB = 3k

હવે, sin A • cosec A = 1

$bold italic s bold italic i bold italic n bold space bold italic A bold space bold equals bold space fraction numerator bold 1 over denominator bold cosec bold space bold A end fraction bold space bold equals bold space fraction numerator bold 1 over denominator square root of bold 10 end fraction bold italic c bold italic o bold italic s bold space bold italic A bold space bold equals bold space fraction numerator bold A bold B over denominator bold A bold C end fraction bold space bold equals bold space fraction numerator bold 3 bold k over denominator square root of bold 10 bold k end fraction bold space bold equals bold space fraction numerator bold 3 over denominator square root of bold 10 end fraction bold space bold space bold italic t bold italic e bold italic n bold space bold italic A bold space bold equals bold space fraction numerator bold B bold C over denominator bold A bold B end fraction bold space bold equals bold space fraction numerator bold k bold space over denominator bold 3 bold k end fraction bold space bold equals bold space bold 1 over bold 3 bold italic s bold italic e bold italic c bold space bold italic A bold space bold equals bold space fraction numerator bold 1 over denominator bold c bold o bold s bold space bold A end fraction bold space bold equals bold space fraction numerator square root of bold 10 over denominator bold 3 end fraction bold space bold અન ે bold space bold italic c bold italic o bold italic t bold space bold italic A bold space bold equals bold space fraction numerator bold 1 over denominator bold t bold e bold n bold space bold A bold space end fraction bold space bold equals bold space bold 3$

∆ABCમાં, B કાટકોણ હોય, BC = 7 અને AC - AB = 1, તો sin C તથા cos C શોધો.

જો cot θ = $bold a over bold b$ , તો $fraction numerator bold cos bold space bold theta bold space bold minus bold space bold sin bold space bold theta over denominator bold cos bold space bold theta bold space bold minus bold space bold sin bold space bold theta end fraction$ નું મૂલ્ય શોધો.

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