How do you perform multiplication and use the fundamental identities to simplify $(2cscx+2)(2cscx-2)$ ?

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Answer 1 · 2017-01-26T19:14:07

see below

$(2 csc x+2) (2csc x-2)=4csc^2x-4cscx+4cscx-4$

$=4csc^2x-cancel (4cscx)+cancel (4cscx)-4$

$=4csc^2 x-4$

$=4(csc^2x-1)$ --> Use the identity $1+cot^2x=csc^2x$

$=4cot^2x$

How do you perform multiplication and use the fundamental identities to simplify (2cscx+2)(2cscx-2)(2cscx+2)(2cscx-2)?