solve online math exam solutions

LEVEL II 1. We know from Napier's analogy that : $\qquad\qquad{\displaystyle \tan\left(\frac{B-C}{2}\right)=\frac{b-c}{b+c}\cot\frac{A}{2}}$ $\qquad\qquad{\displaystyle \tan\left(\frac{A-B}{2}\right)=\frac{a-b}{a+b}\cot\frac{C}{2}}$ $\qquad\qquad{\displaystyle \tan\left(\frac{C-A}{2}\right)=\frac{c-a}{c+a..

Solution

> = . * M [log | sin (x - a) | - log | sin (x - fc) [ ] + c = log + * sm {a - b) sin (a - b) sm (x - b) 11. ^ = f~-dx [For alternative solution see Q. 3 in solved Ex. 21 J1 + cot x J sin x + cos x x 1 = f si" x (cos x - sin x) ^ _ fsin 2x -2sin 2 x ^ J (cos x + sin x) (cos x - sin x) J 2 cos 2x fsin 2x + cos 2x -1 , l'f-2sin2x...

Solution

(0 sin = sin -J = 1 sin"* solved Ex. 1(0 2 2 6 J -1 [ .v^n, tt ..

solution

Trigonometric Functions and Identities LEVEL-I 1. Here L.H.S. $\sin^{2}12^{\circ}+\sin^{2}21^{\circ}+(\sin^{2}39^{\circ}-\sin^{2}9^{\circ})+(\sin^{2}48^{\circ}-\sin^{2}18^{\circ})$ $\Rightarrow\sin^{2}12^{\circ}+\sin^{2}21^{\circ}+\sin(48^{\circ}).\sin(30^{\circ})+\sin(30^{\circ}).\sin(66^{\circ})$ ..

Solution

2. Electronic Configuration A /Rightarrow 2 B /Rightarrow 2,8 C /Rightarrow 2,6 D..

Solutions

The greatest common factor is 8 6Ans : Given equation is xy + 3y 2x 6 = 0 arrange them in an order now. We get xy 2x + 3y 6 = 0 x (y 2) + 3 (y 2) = 0 (x + 3) (y 2) = 0 So here (x + 3) and ( y 2) are the factors 7Ans: Given that. 5(A) +6(O) =$40 Each orange is $3 So we get 5(A) + 6(O) = $40 5(A) + 6(3) = 40 5(A) + 18 ..

Solved problems in principle of mathematical induction

Based on the principle involved in mathematical induction, we are going to solve the problems. The solutions for problems are explained with a specific algorith..

types of solutions

$\frac{dy}{dx}=\mathrm{f}(\mathrm{x})$ and $\frac{dy}{dx}=\mathrm{f}(\mathrm{y})$. To solve the differential equations of the type $\frac{dy}{dx}=\mathrm{f}(\mathrm{x})$, we integrate both sides to get the general solution as discussed below: $\Rightarrow\frac{dy}{dx}=f(x)$ $\Rightarrow dy=f(x)..

general solution

Since, trigonometric functions are periodic, a solution generalised by means of periodicity of the trigonometrical functions. The solution consisting of all possible solutions of a trigonometric equation is called its general solution We use of following results for solving the t..

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