Prove that-tanA-tan B-tan A-tan B-sin A-B-sin A-B

LHS: sin(A+B)/sin(A B) sinA/cosA+sinB/cosB/sinA/cosA sinB/cosB sinAcosB+cosAsinB/cosAcosB/sinAcosB cosAsinB/cosAcosB = sinAcosB+cosAsinB/cosAcosB cosAsinB = sin ...

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Standard XII

Mathematics

Sin(A+B)Sin(A-B)

Prove that:ta...

Question

Prove that:
$\frac{t a n A + t a n B}{t a n A - t a n B} = \frac{s i n (A + B)}{s i n (A - B)}$

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Solution

$L H S : \frac{t a n A + t a n B}{t a n A - t a n B}$
$= \frac{\frac{s i n A}{c o s A} + \frac{s i n B}{c o s B}}{\frac{s i n A}{c o s A} - \frac{s i n B}{c o s B}}$
$= \frac{\frac{s i n A c o s B + c o s A s i n B}{c o s A c o s B}}{\frac{s i n A c o s B - c o s A s i n B}{c o s A c o s B}}$
$= \frac{s i n A c o s B + c o s A s i n B}{c o s A c o s B - c o s A s i n B}$
$= \frac{s i n (A + B)}{s i n (A - B)}$
$∴ \frac{t a n A + t a n B}{t a n A - t a n B} = \frac{s i n (A + B)}{s i n (A - B)}$
Hence proved.

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Similar questions

Prove that tan A + tan÷ tan a - tan b= sin a + b ÷ Sin A - b

Q. Prove that

\frac{\tan A + \tan B}{\tan A - \tan B} = \frac{\sin (A + B)}{\sin (A - B)}

Q. Prove that

tan A + tan B + tan C - tan A tan B tan C = \frac{sin (A + B + C)}{cos A cos B cos C}

\frac{sin (A + B)}{cos A cos B} = tan A + tan B

Q. If

sin (A + B) = 1

and

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\frac{1}{\sqrt{3}}

, find the value of

tan A + tan B

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Prove that: tanA+tanBtanA−tanB=sin(A+B)sin(A−B)

LHS:tanA+tanBtanA−tanB =sinAcosA+sinBcosBsinAcosA−sinBcosB =sinAcosB+cosAsinBcosAcosBsinAcosB−cosAsinBcosAcosB =sinAcosB+cosAsinBcosAcosB−cosAsinB =sin(A+B)sin(A−B) ∴tanA+tanBtanA−tanB=sin(A+B)sin(A−B) Hence proved.

Prove that:
$\frac{t a n A + t a n B}{t a n A - t a n B} = \frac{s i n (A + B)}{s i n (A - B)}$