If A - B - C -180- then -tan A -2tan B -2 is equalA- 3B- 0C- 2D- 1

The correct option is D 1 Given that, A + B + C =180^∘ ⇒A/2+B/2 =90^∘ C/2 ⇒ tan ( A/2+B/2 )= tan ( 90^∘ C/2 ) ⇒ ( tan A/2+ tanB/2 )tan C/2=1 tan A/2 tan ...

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Byju's Answer

Standard XII

Mathematics

Improper Integrals

If A + B + C ...

Question

If A+B +C = $180^{\circ}$ , then $\sum t a n \frac{A}{2} t a n \frac{B}{2}$ is equal

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Solution

The correct option is B
1

Given that, A + B + C = $180^{\circ}$

$\Rightarrow \frac{A}{2} + \frac{B}{2} = 90^{\circ} - \frac{C}{2} \Rightarrow t a n (\frac{A}{2} + \frac{B}{2}) = t a n (90^{\circ} - \frac{C}{2}) \Rightarrow (t a n \frac{A}{2} + t a n \frac{B}{2}) t a n \frac{C}{2} = 1 - t a n \frac{A}{2} t a n \frac{B}{2} \Rightarrow t a n \frac{A}{2} t a n \frac{B}{2} + t a n \frac{B}{2} t a n \frac{C}{2} + t a n \frac{C}{2} t a n \frac{A}{2} = 1$

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If A+B +C =180∘, then ∑tanA2tanB2 is equal

The correct option is B 1 Given that, A + B + C =180∘ ⇒A2+B2=90∘−C2⇒tan(A2+B2)=tan(90∘−C2)⇒(tanA2+tanB2)tanC2=1−tanA2tanB2⇒tanA2tanB2+tanB2tanC2+tanC2tanA2=1

If A+B +C = $180^{\circ}$ , then $\sum t a n \frac{A}{2} t a n \frac{B}{2}$ is equal