Napier’s Analogy

Q. If A=\{1, 2, 3, 4\} and B=\{5, 6, 7\} then A△ B is? what this sign s†an d for " △

Q. If $tan\frac{B-C}{2}=xcot\frac{A}{2},thenx=$

1. $\frac{c-a}{c+a}$
2. $\frac{a-b}{a+b}$
3. $\frac{b-c}{b+c}$
4. None of these

Q.

In a triangle $ABC$ we define
$x=tan\frac{B-C}{2}tan\frac{A}{2},y=tan\frac{C-A}{2}tan\frac{B}{2}$ and $z=tan\frac{AB}{2}tan\frac{C}{2}$
Then the value of $x+y+z$ (in terms of $x,y,z$) is

1. xyz

2. -xyz

3. 2xyz

4. none

Q. If $a,b,c$ are the sides opposite to angles $A,B,C$ of a triangle $ABC,$ respectively and $\angle A=\frac{\pi }{3},b:c=\sqrt{3}+1:2,$ then the value of $\angle B-\angle C$ is

1. $\frac{\pi }{12}$
2. $\frac{\pi }{6}$
3. $\frac{\pi }{4}$
4. $\frac{\pi }{2}$

Q. If in a triangle $ABC,a=5,b=4$ and $\cos (A-B)=\frac{31}{32}$. then the third side $c$ is equal to

1. 3
2. 6
3. 7
4. 9

Q. In a triangle ABC,
$\angle A=60°andb:c=\sqrt{3}+1:2,thenthevalueof\angle B-\angle C=$ .

1. $45°$
2. $60°$
3. $15°$
4. $30°$

Q. 24.If cot^(-1)((2n)/(pi))>(pi)/(3) n in N then number of values of n is (1) 0 (2) 1 (3) 2 (4) 3

Q. In a triangle ABC, a = 6, b = 3 and $\tan \left(\frac{A-B}{2}\right)=\frac{1}{3}$. Area of triangle ABC = sq. units.

1. 4
2. 16
3. 3
4. 9

Q. In $∆ABC,\mathrm{if}a=\sqrt{2},b=\sqrt{3}\mathrm{and}c=\sqrt{5}$, show that its area is $\frac{1}{2}\sqrt{6}\mathrm{sq}.$ units.

Q. Write the value of θ ϵ $\left(0,\frac{\mathrm{\pi }}{2}\right)$ for which area of the triangle formed by points O (0, 0), A (a cos θ, b sin θ) and B (a cos θ, − b sin θ) is maximum.

Q. Q23. ​In a triangle ABC, let angle C=π/2.If r is the inradius and R is the circumradius of the triangle, then 2(r+R) is equal to,
(A). a+b-c (B). b+c (C). c+a (D). a+b+c