If A-B-C- pi find the value of nbsp-tan-A-B-C- nbsp- nbsp- nbsp-tanB nbsp- nbsp- -8203-tanC-tan A-C nbsp- nbsp- nbsp- nbsp- 0 nbsp- nbsp- nbsp- nbsp-tanA-tan A-B nbsp- nbsp- -8203- nbsp- nbsp- nbsp- nbsp- -8203- nbsp- nbsp- -8203-tanA nbsp- 0 nbsp- nbsp- nbsp- nbsp-

Dear Student, A+B+C= #960; #8658;tanA+B+C=0A+C= #960; BtanA+C= tanBSimilarly, #160;tanA+B= tanCtanA+B+CtanBtanCtanA+C0tanAtanA+B tanA0=0tanBtanC tanB0t ...

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Standard IX

Mathematics

Values of Trigonometric Ratios

If A+B+C= pi ...

Question

If A+B+C= pi find the value of
|tan(A+B+C) tanB tanC|
|tan A+C 0 tanA|
|tan A+B -tanA 0 |

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Solution

Dear Student,

$A + B + C = π \Rightarrow \tan (A + B + C) = 0 A + C = π - B \tan (A + C) = - \tan (B) Similarly, \tan (A + B) = - \tan (C) |\begin{matrix} \tan (A + B + C) & \tan (B) & \tan (C) \\ \tan (A + C) & 0 & \tan (A) \\ \tan (A + B) & - \tan (A) & 0 \end{matrix}| = |\begin{matrix} 0 & \tan (B) & \tan (C) \\ - \tan (B) & 0 & \tan (A) \\ - \tan (C) & - \tan (A) & 0 \end{matrix}| which is a skew - symmetric matrix of odd order \Rightarrow \det = 0 OR By expanding = 0 - \tan (B) (\tan (A) \tan (C)) + \tan (C) (\tan (A) \tan (B)) = 0$

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If A+B+C= pi find the value of |tan(A+B+C) tanB ​tanC| |tan A+C 0 tanA| |tan A+B ​ ​ ​-tanA 0 |

Dear Student, A+B+C=π⇒tanA+B+C=0A+C=π-BtanA+C=-tanBSimilarly, tanA+B=-tanCtanA+B+CtanBtanCtanA+C0tanAtanA+B-tanA0=0tanBtanC-tanB0tanA-tanC-tanA0which is a skew-symmetric matrix of odd order⇒det=0ORBy expanding=0-tanBtanAtanC+tanCtanAtanB=0 Regards

If A+B+C= pi find the value of
|tan(A+B+C) tanB tanC|
|tan A+C 0 tanA|
|tan A+B -tanA 0 |