What is the squared root of 14400?
We have to find the square root of 14400 Solution \(\begin{array}{l}\sqrt{14400}\end{array} \) can be expressed as =\(\begin{array}{l}\sqrt{14400}= \sqrt{144 X100}\end{array} \)... View Article
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How do you verify tan (pi – x) = -tanx?
We know the identity tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)] Now we will substitute... View Article
Mention the formula of integration of csc2 x
The formula for integration of csc2 x is given below ∫ csc2 dx = -cot x + C
What is meant by perigee and apogee?
The Moon’s orbit around Earth is elliptical. The point of the orbit closest to Earth is called perigee, while the... View Article
What is the derivative of tan(2x)?
d/dx tan 2x = 2 sec2 (2x) Explanation: We know that the derivative of tan x is sec2 x d/dx... View Article
Prove that tan(π/4 + θ) – tan(π/4 – θ) = 2 tan 2θ
tan(π/4 + θ) – tan(π/4 – θ) = [(tan π/4 + tan )/(1 – tan π/4 tan )] – [(tan... View Article
How do you simplify (2/3)-3?
\(\begin{array}{l}(\frac{2}{3})^{-3}\end{array} \) We will expand using the law of exponents \(\begin{array}{l}(\frac{2}{3})^{-3}=\frac{1}{\frac{2}{3}^{3}}\end{array} \) = \(\begin{array}{l}\frac{3^{3}}{2^{3}}\end{array} \) = 27/8
How do you verify the identity sin(pi/2 + x) = cosx?
Tp prove sin(π/2 + x) = cosx Proof Let us start with LHS sin(π/2 + x) We can express sin... View Article
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... 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... 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... 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 Definition of pi The value of Pi... View Article
What is the derivative of e-2x?
We have to find the derivative of e-2x Solution e-2x \(\begin{array}{l}\frac{\mathrm{d} }{\mathrm{d} x}e^{-2x}\end{array} \) We know that \(\begin{array}{l}\frac{\mathrm{d} }{\mathrm{d} x}e^{nx}=... View Article
How do you prove cos2x = 1 – 2sin2x using other trigonometric identities?
We have to prove \(\begin{array}{l}\cos2x=1-\sin^{2}x\end{array} \) Solution \(\begin{array}{l}\cos2x=1-\sin^{2}x\end{array} \) Let us start with LHS Using the double angle formula we... 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).... 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 =... View Article
How do you simplify cos(sin-1x)?
We have to evaluate \(\begin{array}{l}\cos(\sin^{-1}x)\end{array} \) Solution \(\begin{array}{l}\cos(\sin^{-1}x)\end{array} \) Let us assume \(\begin{array}{l}(\sin^{-1}x)=\Theta\end{array} \) =\(\begin{array}{l}sin\Theta =x\end{array} \) =>\(\begin{array}{l}\sin^{2}\Theta = x^{2}\end{array}... 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... View Article
Multiply square root of 3 and the square root of 6
square root 3 times square root 6 Solution \(\begin{array}{l}\sqrt{3} X \sqrt{6}\end{array} \) We know the value of √3 = 1.732... View Article
