Prove that: - + = A-B 2 - Vidyadip

Question

Prove that:
$\frac{\sin\text{A}-\sin\text{B}}{\cos\text{A}+\cos\text{B}}=\tan\frac{\text{A}-\text{B}}{2}$

✓

Answer

We have,
$\text{LHS}=\frac{\sin\text{A}-\sin\text{B}}{\cos\text{A}+\cos\text{B}}$
$=\ \frac{2\cos\Big(\frac{\text{A}+\text{B}}{2}\Big)\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)}{2\cos\Big(\frac{\text{A}+\text{B}}{2}\Big)\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)}$
$=\ \frac{\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)}{\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)}$
$= \tan\Big(\frac{\text{A}-\text{B}}{2}\Big)$
$=\ \text{RHS}$
$\therefore\ \frac{\sin\text{A}-\sin\text{B}}{\cos\text{A}+\cos\text{B}}=\tan\Big(\frac{\text{A}-\text{B}}{2}\Big).$ Hence proved.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Transformation Formulae→Transformation Formulae — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Coefficient of variation of the two distributions are 60 and 70 and their standard deviations are 21 and 16 respectively. What are their arithmetic means?

The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8. If the first two pH reading are 7.48 and 7.85, find the range of pH value for the third reading that will result in the acidity level being normal.

Find what the following equations become when the origin is shifted to the point $(1, 1).$
$x^2 + xy − 3y^2 − y + 2 = 0$

The angle in one regular polygon is to that in another as 3 : 2 and the number of sides in first is twice that in the second. Determine the number of sides of two polygons.

Convert in the polar form: $\frac{{1 + 7i}}{{{{(2 - i)}^2}}}$

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If there are 640 litres of the 8% solution, how many litres of 2% solution will have to be added?

Find the length of the line$-$segment joining the vertex of the parabola $y^2 = 4ax$ and a point on the parabola where the line$-$segment makes an angle $\theta$ to the $x-$axis.

Write the component statements of the following compound statements and check whether the compound statement is true or false.
24 is a multiple of 4 and 6.

For any two sets A and B, show that the following statements are equevalent:
$\text{A}\cap\text{B}=\text{A}.$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{-\frac{1}{2}}}\frac{8\text{x}^{3}+1}{2\text{x}+1}$