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03 March 2020: The Hindu Analysis

UPSC Current Affairs Preparation: The Hindu Analysis Watch expert analysis of ‘The Hindu’ dated 3rd March 2020. Important news and views to... View Article

Facial Recognition – Uses & Concerns: RSTV – Big Picture

Rajya Sabha TV programs like ‘The Big Picture’, ‘In Depth’ and ‘India’s World’ are informative programs that are important for UPSC preparation.... View Article

Show that: sinA/(secA+tanA-1) + cosA/(cosecA+cotA-1) = 1.

To prove sin A / (sec A + tan A - 1) + cos A / (cosec A + cot A - 1) = 1 Proof LHS = sin A / (sec A + tan A - 1) + cos A / (cosec A + cot A -... View Article

Show that: n^2-1 is divisible by 8, if n is an odd positive integer.

Given that n is an odd positive integer To Prove n2 – 1 is divisible by 8 if n is an odd integer Solution We know that odd number in the... View Article

If d is HCF of 56 and 72, then find x,y satisfying the equation d = 56x + 72y. Also show that x and y are not unique.

Answer: As per Euclid’s division lemma: for any two positive integers, say a and b, there exist unique integers q and r, such that a = bq + r;... View Article

ABCD is a trapezium in which AB II CD. If angle ADC = twice angle ABC, AD = a cm and CD = b cm, then find the length of AB.

We have to determine the length of AB Consider the trapezium ABCD in which AB II CD ABCD is a trapezium with AB || CD. ⇒ angle ( ABC + ADC) =... View Article

Find the value of the integral (1+2cosx)/(2+cosx)^2 dx from 0 to π/2.

Answer: Let us consider Using the identity sin2x + cos2x = 1, ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ Now, = = 1/2 Check out the... View Article

Integrate log(sinx+cosx)dx from -pi/4 to pi/4.

First put x = -x and add On differentiating both sides we get, ⇒ dx = dt / 2 On substituting the values of t and dt in log (cos 2x),... View Article

What is the integration of log (1-x/x) with limit 0 to 1?

Let us assume the given integral as I =0∫1 ( log ((1 - x) / x)dx ----- (1) Using the formula 0∫2af (x) dx = 0∫2a f (x - 2a) dx we will... View Article

Integrate: (1+tanx)dx/(1-tanx).

Let us assume the integral I= {1+tanx/1-tanx}dx I= {1+tanx/1-tanx}dx On expressing the above equation in terms of sin and cos then solving we... View Article

Find the integration of log(cosx) from 0 to π/4.

Take log(cosx) as first function and 1 as second function.... Use integration by parts formula that is ∫f(x).g(x) = f(x).g'(x) -... View Article

Find the integral of ∫cosec x / log(tan x/2) dx.

We have to integrate Let us integrate the given function using the substitution method. In this method of integration by substitution, any... View Article

Find the integral of [tan^-1x]dx from 0 to 102, where [x] is the largest integer not exceeding x.

. . . [102 - (tan 1) ]. Check out the video given below to know more about trigonometry measuring heights and distances Articles to... View Article

What is the value of the integral ∫e^axcos(bx) dx?

Let us solve the given equation by integration by parts. ⇒ I = ∫ eax cos (bx) dx Let, u = eax and v = cos(bx) ∫ uv dx = u ∫ v dx − ∫ u' (∫ v... View Article

Find the integral of (sinx + cosx) / [3+sin2x] dx.

Integral of (sin x + cos x) / 3 + sin 2x dx can be written as: ∫(sin x + cos x)/(3 + sin 2x) dx ∫ (sin x + cos x)dx/(3 + sin 2x) We can... View Article

Integrate sqrt(sinx) with limit 0 to pi/2.

∫√sin(x)dxRewrite/simplify using trigonometric/hyperbolic identities:=∫√2cos^2(2x−π) / [4])−1dx=∫√1−2sin^2(2x−π) / [4])dxSubstitute u=(2x−π) /... View Article

∫(x+sinx)/(1+cosx)dx =

∫ ( x + sin(x)) dx /(1 + cos(x)= ∫ ( x + 2sin(x/2)cos(x/2)) dx /(1 + 2cos^2(x/2) - 1)= ∫ ( x + 2sin(x/2)cos(x/2)) dx / 2cos^2(x/2) = ∫ x dx / 2... View Article

Integrate log(1+tan x) from 0 to pi/4.

Answer: Let us consider We know that ⇒ ⇒ ----------(i) Using the identity tan(a - b) = (tan a - tan b ) /(1 + tan a tan b) we get ⇒... View Article

Integrate {(secx tanx ) / (3secx +5)} dx.

Answer: Given that Let us consider t = 3 sec x + 5 Differentiate t with respect to x Substitute the values of dx in the integration... View Article

If the integral of (sin2x-cos2x)dx = 1/2^[1/2] sin(2x-a)+b, then find a & b.

Let us solve the given equation, LHS and RHS separately ∫(sin 2x - cos 2x) dx = 1/√2(sin(2x - a) + b) Considering LHS = -1/2(cos 2x + sin... View Article

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