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How do you calculate log _10 (2)?

The logarithmic function is defined by: logab = x, then ax = b. Where, x is the logarithm of a number ‘b.’ ‘a’ is the... View Article

Find the general solution tan x = -1/√3

Let us simplify, tan x = -1/√3 tan x = tan (π/6) = tan (-π/6) [since, tan (-x) = -tan x] ∴ the general solution is x = nπ +... View Article

Evaluate tan 90°

Tangent 90 degrees is evaluated as undefined because tan of an angle is equal to the ratio of sin and cos of the same angle. Since, sin 90 = 1... View Article

Mention the formula for integral of cosⁿ x?

∫coshnx dx = (1/n) sinh x coshn−1 x − (n−1/n) ∫coshn−2x dx This formula is known as reduction formula. The... View Article

How do you prove that the circumference of a circle is 2πr?

To derive the formula for circumference let us start with definition of pi The value of Pi (π) is the ratio of the circumference of a circle... View Article

What is the derivative of e^-2x?

We have to find the derivative of e-2x e-2x We know that On using the above formula we get Answer... View Article

How do you prove cos2x = 1 – 2sin²x using other trigonometric identities?

We have to prove Let us start with LHS Using the double angle formula we know that and also from the first trigonometric identity we get... View Article

How do you find the exact value of cos^-1 (-1/2)?

Inverse function is also represented by arc cos-1(-1/2)= arccos(-1/2) arccos(- 1 / 2) Assume y = arccos(- 1 / 2). cos y = – 1 / 2 with 0... View Article

Evaluate cos^-1(0)

Let α is an angle equal to cos-1 (0)α = cos-1(0)We know that, cos 90 degrees = 0Therefore, α = cos-1 (cos 90) = 0 degrees=... View Article

How do you simplify cos(sin^-1x)?

We have to evaluate Let us assume = => => => => On putting this => => On back substitution we get... View Article

Integrate sqrt of (x²-1)/x dx

∫ √(x^2 - 1) dx / x let us assume x = sec u: u = sec-1(x) and tan u = √(x2 - 1) dx = sec u tan u du now the integral becomes... View Article

Multiply square root of 3 and the square root of 6

square root 3 times square root 6 We know the value of √3 = 1.732 and √6 =2.449 On multiplying we get = 4.241668... View Article

What is the limit as x approaches infinity of e^x?

When x takes the value infinity, it becomes. e∞ = ∞ =∞... View Article

Verify that cos 2x = 2 cos2 x -1

------(i) We have learnt that So Substituting in equation (i) we get =... View Article

Solve cos 2θ + sin θ + 1 = 0

cos2θ + sin θ + 1 = 0 ⇒ (1 – sin2θ) + sin θ + 1 = 0 ⇒ sin2θ – sin θ – 2 = 0... View Article

The derivative of cos 3x w.r.t. sin 3is

Let u = cos3x and v = sin3x On differentiating we get = = = =... View Article

What is the tangent ratio at 15 degrees?

Tan (15°) = sin 15/cos 15 Tan 15° = sin 15/cos 15 Sin 15° = sin (45 – 30)° and cos 15 = cos (45 – 30)° ∴... View Article

Simplify (sec²x) – (tan²x) using sin and cos

We know the identity sin2(x)+cos2(x)=1 ——-(i) Dividing throughout the equation by cos2(x) We get sin2(x)/cos2(x) + cos2(x)/cos2(x) =... View Article

sec 2x – tan 2x in terms of tan is _________?

sec 2x – tan 2x (1/cos 2x) – (sin 2x/cos 2x) = (1 – sin 2x)/cos 2x Using the identities, sin2A + cos2A = 1 cos 2A = cos2A... View Article

What is the derivative of f(x) = cos^-1(x) ?

Let us assume y= cos-1x By Differentiate Implicitly -sin y dy/dx= -1-------------(i) By trigonometric identity we know that = = =... View Article

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