Find the value of tan(-135) and cot(-135) along with the steps.
We have to determine the value of tan(-135) and cot(-135) tan(-135) tan(-135) can be expressed as tan (-135º) = tan (360º... View Article
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If sin-1 x + sin-1y + sin-1 z = π, then prove that x√1 – x2 + y√1 – y2 + z√1 – z2 = 2xyz
Given equation sin-1 x + sin-1 y + sin-1 z = π To prove We have to prove x√1 – x2 + y√1 –... View Article
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... View Article
Prove that sin6A+cos6A=1-3sin2Acos2A
Answer: Given sin6A + cos6A sin6A + cos6A = (sin2A)3 + (cos2A)3 (a + b)3 = a3+ b3... View Article
Find the integral of log(sinx+cosx) from -pi/4 to pi/4.
\(\begin{array}{l}I = int_{-pi/4}^{pi/4}log(sinx+cosx)dx\\end{array} \) \(\begin{array}{l}I = int_{-pi/4}^{pi/4}log[sqrt{2}]*[frac{1}{sqrt{2}}sinx+frac{1}{sqrt{2}}cosx]=int_{-pi/4}^{pi/4}log(sqrt{2}sin[x+pi/4])dx\end{array} \) Put x+π/4=t \(\begin{array}{l}I = int_{0}^{pi/2}log[sqrt{2}]sintdt\=int_{0}^{pi/2}log(sqrt{2}+log sintdt\=logsqrt{2}int_{0}^{pi/2}1dt+int_{0}^{pi/2}log sintdt\=pi/2 logsqrt{2}-pi/2 log2\=-pi/4 log2\end{array} \) Check... View Article
Find the value of sin 135.
We have to find the value of sin 135º Solution sin(135) can be expressed as = sin (90 + 45)... 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... 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... 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, …... 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+... 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... 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... 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! +... View Article
Find the remainder when (32^32)^32 is divided by 7.
(3232) 32 Solution The given number is (3232) 32 = (28+4)32) 32 Let us consider (32)32 ^ 32=(32)k=(28+4)k (28+4)k= kC028k40+ kC128k−141+……….+ kCk2804k The expansion... View Article
Find x: √x+√x+√x+……………..∞ = 6.
Given that √x+√x+√x+………infinite terms = 6 Find out We have to find the value of x Solution √(x+6) = 6... View Article
Find the value of x: 2x * 3 x+4 = 7x
log(2x)+log(3 x+4)=log(7x) x∗log(2)+(x+4)∗log(3)=x∗log(7) Simplifying a little bit more, x∗log(2)+x∗log(3)+4log(3)=x∗log(7) x(log(7)−log(2)−log(3))=4log(3) x=4log(3)log(7)−log(2)−log(3) We know that the values of log(2)=0.3010 log(3)=0.4771 log(7)=0.8451 On... View Article
Explain how to make six 9’s equal to 100
Six 9’s equal to 100 can be expressed in the following ways 9 × 9 + 9 + 9 +... View Article
What is the derivative of y = (1-x)(2-x)….(n-x) at x=1?
Derivative of y=(1-x)(2-x)…….(n-x) We need to find the derivative of y = (1 – x)(2 – x)…….(n – x) Solution... View Article
