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# How to Pursue Mathematics after High School?

For Students who are passionate for Mathematics and want to pursue it for higher studies in India and abroad.

This is a beautiful problem from ISI MStat 2019 PSA problem 12 based on finding the domain of the function. We provide sequential hints so that you can try.

## Domain of a function- ISI MStat Year 2019 PSA Question 12

What is the set of numbers $x$ in $(0,2 \pi)$ such that $\log \log (\sin x+\cos x)$ is well-defined?

• $[\frac{\pi}{8},\frac{3 \pi}{8}]$
• $(0,\frac{\pi}{2})$
• $(0,\frac{ \pi}{4}]$
• $(0,\pi) \cup (\frac{3 \pi}{2}, 2 \pi)$

### Key Concepts

Domain

Basic inequality

Trigonometry

Answer: is $(0,\frac{\pi}{2})$

ISI MStat 2019 PSA Problem 12

Pre-college Mathematics

## Try with Hints

$logx$ is defined for $x \in (0,\infty)$.

$sinx+cosx > 0$.
$log(sinx+cosx) > 0 \Rightarrow sinx + cosx > 1$
$sin(x+\frac{\pi}{4}) > \frac{1}{\sqrt{2}}$
For $y$ in $(0,2 \pi)$ , $siny > \frac{1}{\sqrt{2}} \iff \frac{\pi}{4} < y < \frac{3\pi}{4 }$

Hence we have $0< x < \frac{\pi}{2 }$ .

## What to do to shape your Career in Mathematics after 12th?

From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here:

• What are some of the best colleges for Mathematics that you can aim to apply for after high school?
• How can you strategically opt for less known colleges and prepare yourself for the best universities in India or Abroad for your Masters or Ph.D. Programs?
• What are the best universities for MS, MMath, and Ph.D. Programs in India?
• What topics in Mathematics are really needed to crack some great Masters or Ph.D. level entrances?
• How can you pursue a Ph.D. in Mathematics outside India?
• What are the 5 ways Cheenta can help you to pursue Higher Mathematics in India and abroad?

## Want to Explore Advanced Mathematics at Cheenta?

Cheenta has taken an initiative of helping College and High School Passout Students with its "Open Seminars" and "Open for all Math Camps". These events are extremely useful for students who are really passionate for Mathematic and want to pursue their career in it.

To Explore and Experience Advanced Mathematics at Cheenta

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