New india @70and your contribution essay
Answers
India after 70 years of independence indeed is a land of opportunities and challenges. India is one of the most richly endowed countries in the world. There is enough of everything in it. Mountains, hills, valleys, lakes, deserts, plateaus, seas, plains and whatnot, India has everything. Life sustaining resources such as air, water, sunlight, forests, animals, land, seas, flora, fauna, minerals, metals, human population, etc. exist in staggering abundance. Rivers such as Ganges, Sutlej, Ravi, Beas, Brahmputra, Kaveri, etc. flow perennially through its various planes making them the most fertile and arable planes in the world. Industrious farmers grow all types of crops, vegetables, fruits, etc on these plains and keep the food supplies abundantly supplied throughout the year. So, there is no scarcity of any sort in Indian subcontinent. According to statistics in Wikipedia the total cultivable area in India is 1,945,355 km² (56.78% of its total land area). India has a total water surface area of 360,400 km². India has the 4th largest coal reserves in the world; iron and manganese ores are 7th largest reserve in the world as in 2013; mica and bauxite are 5th largest reserve in the world as in 2013.
Unquestionably, there are many challenges in this wonderful country. Challenges such as population, environmental degradation, poverty of rural people, corruption, backwardness, etc; but these challenges are opportunities too. We can contribute to this change for the betterment by giving our best. Each one of us must do our job and responsibilities perfectly. If each one of us becomes efficient in our sphere of actions, India will automatically become best. All the challenges can easily be overcome provided the entire manpower and resources are utilized and used optimally under the right guidance of dedicated leaders. India can do wonders. India will do wonders surely. And that will happen only when the Indians set their hearts to make India the land of opportunities, growth, and prosperity with their words, deeds, and acts.
We can contribute to this change for the betterment by giving our best. Each one of us must do our job and responsibilities perfectly. All the challenges can easily be overcome provided the entire manpower and resources are utilized and used optimally under the right guidance of dedicated leaders. India can do wonders. India will do wonders surely. And that will happen only when the Indians set their hearts to make India the land of opportunities, growth, and prosperity with their words, deeds, and acts.
If a nation is to achieve invincible prosperity in the fields of health, finances, science, technology, and innovation, the people of that nation must adopt the principle of integrity as it is a divine quality; it augments energy, enthusiasm, creativity, fearlessness, purposefulness, and accomplishment. Applying integrity even in the minutest details, they must persevere in the fields above mentioned.
We can contribute to the making of new India by being excellent in our respective spheres of actions. Besides being perfect in our fields, we must be ideal citizens. We must pay our taxes honestly; we must not do anything that might affect our country’s prosperity and development. We must dedicate ourselves to the progress and development of our country, only then something substantial will happen.
Answer:
Explanation:
\orange{\bold{\underbrace{\overbrace{❥Question᎓}}}}
❥Question᎓
Integrate the function
\huge\green\tt\frac{ \sqrt{tanx} }{sinxcosx}}
⇛\huge\tt\frac{ \sqrt{tanx} }{sinxcosx}
sinxcosx
tanx
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⇛\huge\tt \frac{ \sqrt{tanx} }{sinxcosx \times \frac{cosx}{cosx}}
sinxcosx×
cosx
cosx
tanx
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⇛\huge\tt \frac{ \sqrt{tanx} }{sinx \times \frac{ {cos}^{2} x}{cosx}}
sinx×
cosx
cos
2
x
tanx
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⇛ \huge\tt\frac{ \sqrt{tanx} }{ {cos}^{2} x \times \frac{sinx}{cosx} }
cos
2
x×
cosx
sinx
tanx
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⇛\huge\tt\frac{ \sqrt{tanx} }{ {cos}^{2}x \times tanx }
cos
2
x×tanx
tanx
⇛\huge\tt {tan}^{ \frac{1}{2} - 1 } \times \frac{1}{ {cos}^{2} x}tan
2
1
−1
×
cos
2
x
1
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⇛\huge\tt {(tan)}^{ - \frac{ 1}{2} } \times \frac{1}{ {cos}^{2}x } = {(tanx)}^{ - \frac{1}{2} } \times {sec}^{2} x⇛(tan)(tan)
−
2
1
×
cos
2
x
1
=(tanx)
−
2
1
×sec
2
x⇛(tan)
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⇛\huge\tt {(tan)}^{ - \frac{ 1}{2} } \times \frac{1}{ {cos}^{2}x } = ∫ {(tanx)}^{ - \frac{1}{2} } \times {sec}^{2} x \times dx⇛(tan)(tan)
−
2
1
×
cos
2
x
1
=∫(tanx)
−
2
1
×sec
2
x×dx⇛(tan)
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\bold\blue{☛\: Let tanx=t}☛Lettanx=t
\bold\blue{☛ \:Differentiating \: both \: sides \: w.r.t.x}☛Differentiatingbothsidesw.r.t.x
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⇛\huge\tt {sec}^{2} x = \frac{dt}{dx}sec
2
x=
dx
dt
⇛\huge\tt{dx \frac{dt}{ {sec}^{2}x }}dx
sec
2
x
dt
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⇛\huge\tt∴∫ {(tanx)}^{ - \frac{1}{2} } \times {sec}^{2} x \times dx∴∫(tanx)
−
2
1
×sec
2
x×dx
⇛\huge\tt ∫ {(t)}^{ - \frac{1}{2} } \times {sec}^{2} x \times \frac{dt}{ {sec}^{2}x }∫(t)
−
2
1
×sec
2
x×
sec
2
x
dt
⇛\huge\tt ∫ {t}^{ - \frac{1}{2} }∫t
−
2
1
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⇛ \huge\tt\frac{ {t}^{ - \frac{1}{2} + 1} }{ - \frac{1}{2} + 1 }
−
2
1
+1
t
−
2
1
+1
⇛ \huge\tt \frac{ {t}^{ \frac{1}{2} } }{ \frac{1}{2} } + c = 2 {t}^{ \frac{1}{2} } + c = 2 \sqrt{t}
2
1
t
2
1
+c=2t
2
1
+c=2
t
⇛\huge2 \sqrt{t} + c = 2 \sqrt{tanx}2
t
+c=2
tanx
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