If sin A - n sin B- then n -1- n -1tan A - B -2-A- A-B-2B- sinA-B-2C- tanA 2- B-2D- None of these

The correct option is C We have sin A=n sin B ⇒n/1=sin A/sin B ⇒n 1/n+1=sin A sin B/sin A+sin B=2 cosA+B/2sinA B/2/2 sinA+B/2cosA B/2 =tanA B/2cotA+B/2 ⇒n 1/ ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

If sin A = n ...

Question

If $s i n A = n s i n B, t h e n \frac{n - 1}{n + 1} t a n \frac{A + B}{2} =$

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Solution

The correct option is B

We have $s i n A = n s i n B \Rightarrow \frac{n}{1} = \frac{s i n A}{s i n B}$
$\Rightarrow \frac{n - 1}{n + 1} = \frac{s i n A - s i n B}{s i n A + s i n B} = \frac{2 c o s \frac{A + B}{2} s i n \frac{A - B}{2}}{2 s i n \frac{A + B}{2} c o s \frac{A - B}{2}}$
$= t a n \frac{A - B}{2} c o t \frac{A + B}{2}$
$\Rightarrow \frac{n - 1}{n + 1} t a n (\frac{A + B}{2}) = t a n \frac{A - B}{2} .$

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