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Class 10 Class 12

ત્રિકોણમિતિ

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

∆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 m∠C = 90 લઈએ.

અહીં, ten A = $fraction numerator bold 1 over denominator square root of bold 3 end fraction$

$bold ten bold space bold A bold space bold equals bold space bold BC over bold AC bold space bold equals bold space fraction numerator bold 1 over denominator square root of bold 3 end fraction bold BC over bold 1 bold space bold equals bold space fraction numerator bold AC over denominator square root of bold 3 end fraction bold space bold equals bold space bold k bold space bold left parenthesis bold ધ ા ર ો bold space bold ક ે bold right parenthesis bold space bold જ ્ ય ાં bold space bold comma bold space bold k bold space bold greater than bold space bold 0 bold space bold AC bold space bold equals bold space square root of bold 3 bold space bold k bold space bold અન ે bold space bold BC bold space bold equals bold space bold k bold space$

હવે પાયથાગોરસના પ્રમેય પરથી,

AB² = AC² + BC²

AB² = ( $square root of bold 3$ k)² + k²

= 3k² + k²

= 4k²

AB = 2k (k > 0)

આમ, AC $square root of bold 3$ k, BC = k અને AB = 2k

sin A = $bold BC over bold AB bold space bold equals bold space fraction numerator bold k over denominator bold 2 bold k end fraction bold equals bold space bold 1 over bold 2 bold space bold અન ે bold space bold cos bold space bold B bold space bold equals bold space bold BC over bold AB bold space bold equals bold space bold 1 over bold 2$

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

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.

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

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