Question

Solve This !!!!!!!!!!!!!!!!​

Answer 1

$\huge{\underline{\underline{\sf{Answer :}}}}}$

Given that,

$\sf{cosec \: x \: + sin \: x = 5 \frac{1}{5} } \\ \\ \implies \: \sf{cosec \: x \: + sin \: x = \frac{26}{5} }...........(1)$

Now,

$\sf{ \cosec {}^{2} x + sin {}^{2}x }$

Adding and subtracting 2,we get:

$\rightarrow \: \sf{(cosec{}^{2}x + sin{}^{2}x +2) - 2 } \\ \\ \rightarrow \: \sf{(cosec \: x + \: sin \: x) {}^{2} - 2 }$

From equation (1), we get:

$\rightarrow \: \sf{ (\frac{26}{5}) {}^{2} - 2 } \\ \\ \rightarrow \: \sf{ \frac{676}{25} - 2 } \\ \\ \rightarrow \: \underline{ \boxed{\sf{ \frac{626}{25} }}}$

NOTE

We know that sin∅ = 1/cosec∅

Thus,

sin∅.cosec∅ would be 1

• When expanding (sin∅ + cosec∅)²,we get sin²∅ + cosec²∅ + 2sin∅cosec∅

• At last,this can also be written as sin²∅ + cosec²∅ + 2

Answer 2

Answer:

See the attachment for the answer