\(\begin{array}{l}(1-cos x)(1+cos x)\end{array} \) On multiplying using the identity \(\begin{array}{l}(a-b)(a+b)=a^{2}-b^{2}\end{array} \) we get the equation as \(\begin{array}{l}(1-cos x)(1+cosx)=1-cos^{2}x\end{array} \) \(\begin{array}{l}sin... View Article
We have to differentiate y=lnx y = ln x x=ey dx/dy= ey dy / dx = 1/ey=1/x
We know that tan can be expressed as tan x = sin x / cos x tan (90+x) = sin... View Article
Yes adjacent angles of a parallelogram are supplementary Proof Let us consider Parallelogram ABCD. To prove: ∠A + ∠B =... View Article
log(x)=-0.123 We know that C =logba The inverse relation is a=bc For common logarithms, b =10 So x=10-0.123= 0.7534
We have to factorise 2x2−5x+3=0 We will use splitting the middle term method Split the middle term by finding two... View Article
sin(pi/3) We know that pi=π=180 degrees π/3=120 degrees sin (π/3)=sin 120 degrees sin 120= We know that 180° – 60°... View Article
We have to prove \(\begin{array}{l}\cos 2x =2\cos ^{2}x -1\end{array} \) using the identity \(\begin{array}{l}\cos 2x =\cos ^{2}x -\sin ^{2}x\end{array} \)... View Article
Will solve sin x =1/2 using inverse function so sin-1(1/2) = x Let x is an angle equal to Sin-1... View Article
Equation of the line passing through the points (x1, y1) and (x2, y2) is \(\begin{array}{l}y-{{y}_{1}}=\frac{{{y}_{1}}-{{y}_{2}}}{{{x}_{1}}-{{x}_{2}}}\left( x-{{x}_{1}} \right)\end{array} \) Hence equation... View Article
\(\begin{array}{l}\frac{1}{4^{-2}}=\frac{1}{\frac{1}{4^{2}}}\end{array} \) We know that 42 = 16. so multiply the denominator and numerator by the reciprocal \(\begin{array}{l}\frac{1}{\frac{1}{4^{2}}}=\frac{1. \frac{16}{1}}{\frac{1}{16}.\frac{16}{1}}\end{array} \)... View Article
We have to find the diagonal of a rectangle whose sides are 20 and 48. Solution Let us assume that... View Article
The integers which can be generated by multiplying the two smallest positive integers and contain at least one divisor other... View Article
A dipole moment arises in any system in which there is a separation of charge. They can, therefore, arise in... View Article
We have to factorise sin3x – cos3x Solution \(\begin{array}{l}\sin ^{3}x -\cos ^{3}x\end{array} \) Let us solve using the identity (a3... View Article
A trapezium is not a parallelogram because a parallelogram has 2 pairs of parallel sides. But a trapezium only has... View Article
Square root of a number is the value that returns the original number on multiplied by itself. Finding square root... View Article
Factorial is a multiplication operation of natural numbers with all the natural numbers that are less than it. Formula The... View Article
If an integral has upper and lower limits, it is called a Definite Integral. There are many definite integral formulas... View Article
log 12= log 2x 2 x 3 = log 2 x 2 +log 3 =log 22+ log 3 = 2... View Article
