Archives

Show that cot(a+b)= cotacotb-1 / cota+cotb.

Let us solve the LHS of the equation cot (A + B) We know that cot x = cos x / sin x Hence we will express thegiven LHSin terms of sin and cos... View Article

Prove that sin⁶A+cos⁶A=1-3sin²Acos²A

Answer: Given sin6A + cos6A sin6A + cos6A = (sin2A)3 + (cos2A)3 (a + b)3 = a3+ b3 + 3ab (sin2A + cos2A)3 =... View Article

Find the integral of log(sinx+cosx) from -pi/4 to pi/4.

Put x+π/4=t Check out the video given below to know more about trigonometry measuring heights and distances Articles to explore How do... View Article

Find the value of sin 135.

We have to find the value of sin 135º sin(135) can be expressed as = sin (90 + 45) Using the identity sin(A + B) = sin(A)cos(B) + cos(A)sin(B)... View Article

Define componendo and dividendo along with their applications in mathematics.

Componendo and dividendo is a rule on ratio and proportions that is used to perform calculations and reduce the number of steps can be termed as... View Article

What is the sum of the series 1/1 + (1/1+2) + (1/1+2+3)+…… equal to?

1/1 + 1/3 + 1/6 + 1/10 + …………. 1/k =?Here each term can be written with a pattern as follows:1st term : (2/1) - (2/2) = 1/12nd term : (2/2) - (... View Article

Find the value of n≥1, n^3 – (n-1)^3 + ……….+ (-1)^n-1 1^3 =…………for any odd integer.

Since n is an odd integer, (-1)^n-1 = 1 and n – 1, n – 3, n – 5, … are even integers.We haven^3 + (n – 1)^3 + (n – 2)^3 – (n – 3)^3 + …. + (-1)^n... View Article

If x+1/x =5 and x ²+ 1/x³=8 then find x ³+ 1/x ².

Given We are given that x+1/x =5 x 2+ 1/x3=8 Find out We have to determine the value of x 3+ 1/x 2. x+1/x = 5 On squaring both sides we... View Article

What are the coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0?

Let us consider ax+by+c=0 be a straight line. When a perpendicular line is drawn from any point on the plane to this straight line then the... View Article

If f (x) = x-1/x+1 then find the value of f (2x).

A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has... View Article

If a+b+c+d=4 then find the value of 1/(1-a)(1-b)( 1-c)+1/(1-b) (1-c) (1-d)+1/(1-c) (1-d) (1-a)+1/(1-d)( 1-b) (1-a) .

Given a+b+c+d=4 Fine out We have to determine the value of 1/(1-a)(1-b)( 1-c)+1/(1-b) (1-c) (1-d)+1/(1-c) (1-d) (1-a)+1/(1-d)( 1-b) (1-a) .... View Article

On which axis does the complex number z=x+iy which satisfy the equation mod(z-5i/z+5i) lie?

Given equation |(z-5i)/(z+5i)| = 1 Complex number z=x+iy On substituting z = x+iy in given equation, we get |(x+iy-5i)/(x+iy+5i)| = 1... View Article

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is

The number of derrangements of 6 = 6! (1 – 1/1! + 1/2! - 1/3! + 1/4! – 1/5! + 1/6!) = 360 – 120 + 30 – 6 + 1 = 265 Out of these derangements,... View Article

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Archives

Show that cot(a+b)= cotacotb-1 / cota+cotb.

Prove that sin⁶A+cos⁶A=1-3sin²Acos²A

Find the integral of log(sinx+cosx) from -pi/4 to pi/4.

Find the value of sin 135.

Define componendo and dividendo along with their applications in mathematics.

What is the sum of the series 1/1 + (1/1+2) + (1/1+2+3)+…… equal to?

Find the value of n≥1, n^3 – (n-1)^3 + ……….+ (-1)^n-1 1^3 =…………for any odd integer.

If x+1/x =5 and x ²+ 1/x³=8 then find x ³+ 1/x ².

What are the coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0?

If f (x) = x-1/x+1 then find the value of f (2x).

If a+b+c+d=4 then find the value of 1/(1-a)(1-b)( 1-c)+1/(1-b) (1-c) (1-d)+1/(1-c) (1-d) (1-a)+1/(1-d)( 1-b) (1-a) .

On which axis does the complex number z=x+iy which satisfy the equation mod(z-5i/z+5i) lie?

Find the remainder when (32^32)^32 is divided by 7.

Find x: √x+√x+√x+……………..∞ = 6.

Find the value of x: 2^x * 3 ^x+4 = 7^x

Explain how to make six 9’s equal to 100

What is the derivative of y = (1-x)(2-x)….(n-x) at x=1?

Write the formula to find the number of onto functions from set A to set B.

Explain the procedure to find (d2y/dx2) [second order derivative] of any function y=f(x).

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