Question

Why do we have nightmares?

Answer 1

There can be a number of psychological triggers that cause nightmares . For example, anxiety and depression can cause nightmares. 
nightmares can be caused due to
Different sleep positions 
Your sleep environment
Anxiety and stress can be the reason 
Eating before you sleep
More than required amount of Spicy and unhealthy foods
Drinking alcohol before you sleep 
Drugs can be the reason 
Nightmares can come from illness

Answer 2

Answer:

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Explanation:

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

ㅤ ㅤ ㅤ ㅤ ㅤ

⇛\huge\tt \frac{ \sqrt{tanx} }{sinxcosx \times \frac{cosx}{cosx}}

sinxcosx×

cosx

cosx

tanx

ㅤ ㅤ ㅤ ㅤ ㅤ

⇛\huge\tt \frac{ \sqrt{tanx} }{sinx \times \frac{ {cos}^{2} x}{cosx}}

sinx×

cosx

cos

2

x

tanx

ㅤ ㅤ ㅤ

⇛ \huge\tt\frac{ \sqrt{tanx} }{ {cos}^{2} x \times \frac{sinx}{cosx} }

cos

2

x×

cosx

sinx

tanx

ㅤ ㅤ ㅤ ㅤ ㅤ

⇛\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

ㅤ ㅤ ㅤ ㅤ ㅤ

⇛\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)

ㅤ ㅤ ㅤ ㅤ ㅤ

⇛\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)

ㅤ ㅤ ㅤ ㅤ ㅤ

\bold\blue{☛\: Let tanx=t}☛Lettanx=t

\bold\blue{☛ \:Differentiating \: both \: sides \: w.r.t.x}☛Differentiatingbothsidesw.r.t.x

ㅤ ㅤ ㅤ ㅤ ㅤ

⇛\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

ㅤ ㅤ ㅤ ㅤ ㅤ

⇛\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

−