If s i n x + c o s e c x = 2 , then s i n n x + c o s e c n x is equal to Options: A . &nbsp 2 B . &nbsp 1 C . &nbsp 2 n − 1 D . &nbsp 2 n − 2

Answer: Option A : A s i n x + c o s e c x = 2 ⇒ ( s i n x − 1 ) 2 = 0 ⇒ s i n x = 1 ∴ s i n n x + c o s e c n x = 1 + 1 = 2

If sinx+cosecx=2, then sinnx+cosecnx is equal to

Question -

If $s i n x + c o s e c x = 2$ , then $s i n^{n} x + c o s e c^{n} x$ is equal to

Options:

A . 2

B . 1

C .

2^{n - 1}

D .

2^{n - 2}

Answer: Option A
:
A

$s i n x + c o s e c x = 2 \Rightarrow (s i n x - 1)^{2} = 0 \Rightarrow s i n x = 1$
$∴ s i n^{n} x + c o s e c^{n} x = 1 + 1 = 2$

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