If A - B - C - and cos A -cos B cos C- then tan B tan C is equal toA- 2 B- 1C- -1-2D- 1-2

The correct option is A cos[π (B+C)]=cos B cos C ⇒ cos(B+C)=cos B cos C ⇒ [cos B cos C sin B sin C]=cos B cos C ⇒ sin B sin C=2cos B cos C ⇒ tan B tan C= ...

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Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

If A + B + C ...

Question

If A + B + C = $π$ and cos A = cos B cos C, then tan B tan C is equal to

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Solution

The correct option is B

$c o s [π - (B + C)] = c o s B c o s C \Rightarrow - c o s (B + C) = c o s B c o s C \Rightarrow - [c o s B c o s C - s i n B s i n C] = c o s B c o s C \Rightarrow s i n B s i n C = 2 c o s B c o s C \Rightarrow t a n B t a n C = 2$

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Similar questions

Q. If

A + B + C = π

and

cos A = cos B cos C

, show that

tan A = tan B + tan C

Q. If A + B + C = π, then

\frac{\tan A + \tan B + \tan C}{\tan A \tan B \tan C}

is equal to
(a) tan A tan B tan C
(b) 0
(c) 1
(d) None of these

Q. If

A + B + C = π

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∣ ∣ ∣ ∣ ∣ \begin{matrix} s i n (A + B + C) & s i n B & c o s C - s i n B & 0 & t a n A c o s (A + B) & - t n a A & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣

is equal to

Q. If

A + B + C = π

and cosA=cosB cosC, then tanB tanC is equal to

Q. If

A + B + C = π

and

cos A = cos B cos C

, then

tan B tan C

is equal to

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If A + B + C = π and cos A = cos B cos C, then tan B tan C is equal to

The correct option is B cos[π−(B+C)]=cos B cos C⇒−cos(B+C)=cos B cos C⇒−[cos B cos C−sin B sin C]=cos B cos C⇒sin B sin C=2cos B cos C⇒tan B tan C=2

If A + B + C = $π$ and cos A = cos B cos C, then tan B tan C is equal to

The correct option is B

$c o s [π - (B + C)] = c o s B c o s C \Rightarrow - c o s (B + C) = c o s B c o s C \Rightarrow - [c o s B c o s C - s i n B s i n C] = c o s B c o s C \Rightarrow s i n B s i n C = 2 c o s B c o s C \Rightarrow t a n B t a n C = 2$