Question

If sin θ = x and sec θ = y, then find the value of cot θ.

Answer 1

Answer:

cot∅=1/xy

Step-by-step explanation:

sin∅=x

sec∅=y

sec∅=1/cos∅

So, cos∅=1/y

tan∅=sin∅/cos∅=x/(1/y)=xy

cot∅=1/tan∅=1/xy

Answer 2

Answer:

$\huge{\boxed{\boxed{\sf{\cot(θ) = \frac{1}{xy}}}}}$

Step-by-step explanation:

$\huge{\boxed{\boxed{\underline{\sf{SOLUTION-}}}}}$

>> sin θ = x (given)

>>sec θ = y, (given)

$= ) \sec(θ) = \frac{1}{ \cos(θ) } \\ = )y = \frac{1}{ \cos(θ) } \\ = ) \cos(θ) = \frac{1}{y}$

>>ACCORDING TO THE QUESTION

>> WE HAVE TO FIND THE VALUE OF

=) cot θ = ?

$= ) \cot(θ) = \frac{ \cos(θ) }{ \sin(θ) } \\ = ) \cot(θ) = \frac{ \frac{1}{y} }{x} \\ = ) \cot(θ) = \frac{1}{xy}$

$\huge{\boxed{\boxed{\sf{\cot(θ) = \frac{1}{xy}}}}}$