How do you simplify $sin^2 B sec^2 B - sec^2 B$ ?

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Answer 1 · 2018-03-15T23:22:34

-1

Given: $sin^2Bsec^2B-sec^2B$

Apply the reciprocal identity:
$secB=1/cosB$

So: $sin^2B*1/cos^2B-sec^2B$
$sin^2B/cos^2B-sec^2B$

Apply the quotient identity:
$sinB/cosB= TanB$

So: $tan^2B-sec^2B$

Now apply the Pythagorean identity:
$1+tan^2B=sec^2B$
Manipulated to: $-1=tan^2B-sec^2B$

So: $tan^2B-sec^2B= -1$

How do you simplify sin^2 B sec^2 B - sec^2 Bsin^2 B sec^2 B - sec^2 B?