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One day, two best friends met at their usual hangout place. They talked about everything under the sun, and the topic changed to one of their classmates at school. The so-called classmate excelled in singing, and the first friend admitted that in her case, she isn't a good singer. To this, the second friend replied that no one is a born singer, and one can acquire the skill through constant practice. With this conversation, it is evident that mindset sounds simple, but it is an intensely

Here find the proof of integral of tan x is integral of sec x + C where C is a constant with alternative solutions.  

Solution 1 - Integral of tan x is:

I=∫tan(x)dx

=∫sin(x)cos(x)dx

Assume, u=cos(x)

⟹du=d dx cos(x)dx

⟹du=−sin(x)dx

⟹−du=sin(x)dx

Substitution of x in I gives us,

I=∫−1u du

=−ln(|u|)

Substitution of u, gives us,

I=−ln (|cos(x)|)+C

Solution 2

(integral) tan x dx = - ln |COs x| + C

= ln | (COs x)-1 | + C

= ln |sec x| + C

Hence,

(integral) tan x dx = - ln |COs x| + C

= ln |sec x| + C

Solution 3

(integral) tan

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Mathematics can be described as"the abstract science of number, quantity, and space" while Physics is known as "the branch of science concerned with the nature and properties of matter and energy." Physics makes use of Mathematics. Equations, Formulas and numerical concepts are the basic things in Physics.

Equations and terms of math are similar to that of Physics. Hence if you are someone who scores an A-grade in Math, then you can score in Physics too. Physics at a higher level needs a lot of application of

Being the primary language of various countries, English is one of the most widely spoken languages in the world. Being the chief language of countries like Canada, United States, United Kingdom, Australia, New Zealand etc, English plays a significant role in our day-to-day lives. English is an ever-evolving language.

Presently English is used as an official language in India. English emerged as a second language in a country like India. In schools, English is taught as a foreign language and more and these days more students opt