why India is considered as a mega-diversity nation ? what do understand by endangered and endemic species? write a short note on biosphere reserve. (10+5+5)​

[tex]\large\underline{\sf{Solution-}}[/tex]

Given expression is

[tex]\rm \: L( \: sin2t \: sin3t \: ) \\ \\ [/tex]

can be rewritten as

[tex]\rm \: = \: \dfrac{1}{2} L( \: 2 \: sin2t \: sin3t \: ) \\ \\ [/tex]

We know,

[tex]\boxed{ \rm{ \:2 \: sinx \: siny \: = \: cos(x - y) \: - \: cos(x + y) \: }} \\ \\ [/tex]

So, using this result, we get

[tex]\rm \: = \: \dfrac{1}{2} \: L\bigg[\: cos(2t - 3t) - cos(3t + 2t) \: \bigg] \\ \\ [/tex]

[tex]\rm \: = \: \dfrac{1}{2} \: L\bigg[\: cos( - t) - cos(5t) \: \bigg] \\ \\ [/tex]

[tex]\rm \: = \: \dfrac{1}{2} \: L\bigg[\: cos(t) - cos(5t) \: \bigg] \\ \\ [/tex]

We know,

[tex]\boxed{ \rm{ \:L(cosat) \: = \: \dfrac{s}{ {s}^{2} + {a}^{2} } \: }} \\ \\ [/tex]

So, using this result, we get

[tex]\rm \: = \: \dfrac{1}{2} \bigg(\dfrac{s}{ {s}^{2} + {1}^{2} } - \dfrac{s}{ {s}^{2} + {5}^{2} } \bigg) \\ \\ [/tex]

[tex]\rm \: = \: \dfrac{1}{2} \bigg(\dfrac{s}{ {s}^{2}+1} - \dfrac{s}{ {s}^{2}+ 25} \bigg) \\ \\ [/tex]

Hence,

[tex]\rm\implies \boxed{ \rm{L( \: sin2t \: sin3t \: )=\dfrac{1}{2} \bigg(\dfrac{s}{ {s}^{2}+1}-\dfrac{s}{ {s}^{2}+ 25} \bigg) \: }} \\ \\ [/tex]

[tex]\rule{190pt}{2pt} \\ [/tex]

[tex] { \red{ \mathfrak{Additional\:Information}}}[/tex]

[tex]\boxed{ \rm{ \:L( {e}^{at}) = \frac{1}{s - a} \: }} \\ [/tex]

[tex]\boxed{ \rm{ \:L( {e}^{ - at}) = \frac{1}{s + a} \: }} \\ [/tex]

[tex]\boxed{ \rm{ \:L( sinat) = \frac{a}{ {s}^{2} + {a}^{2} } \: }} \\ [/tex]

[tex]\boxed{ \rm{ \:L( {e}^{bt} sinat) = \frac{a}{ {(s - b)}^{2} + {a}^{2} } \: }} \\ [/tex]

[tex]\boxed{ \rm{ \:L( {e}^{bt} cosat) \: = \: \dfrac{s}{ {(s - b)}^{2} + {a}^{2} } \: }} \\ \\ [/tex]

Answer:Kolkata is located on which river -

Kolkata is the capital of the Indian state of West Bengal. Located on the east bank of the Hooghly River approximately 80 kilometers (50 mi) west of the border with Bangladesh, it is the principal commercial, cultural, and educational center of East India, while the Port of Kolkata is India's oldest operating port and its sole major riverine port.

Answer:

Hooghly: Kolkata is situated on the Hooghly stream. Hugli River, Hugli additionally spelled Hooghly, stream in West Bengal state, northeastern India. An arm of the Ganges (Ganga) River, it gives admittance to Kolkata (Calcutta) from the Bay of Bengal.

*Explanation*-

The river name is: Hooghly in culcatta or Kolkata. The city's location along the banksof the river so near the Bay makes it the most important port city in the country.

Answer:

pitaji pratidin samachar Patra padhte Hain translation

Answer:

look like Crook

Explanation:

Mr Nath look like because of scars of his face