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iris [78.8K]
3 years ago
9

Simplify: sec(θ) sin(θ) cot(θ)

Mathematics
2 answers:
krek1111 [17]3 years ago
4 0

We have to simplify

sec(θ) sin(θ) cot(θ)

Now first of all let's simplify these separately , using reciprocal identities.

Sec(θ) = 1/cos(θ)

Sin(θ) is already simplified

Cot(θ)= cos(θ) / sin(θ) ,

Let's plug these values in the expression

sec(θ) sin(θ) cot(θ)

= ( 1/cos(θ) ) * ( sin(θ) ) * ( cos(θ) / sin(θ) )

= ( sin(θ) /cos(θ) ) * ( cos(θ) /sin(θ) )

sin cancels out with sin and cos cancels out with cos

So , answer comes out to be

=( sin(θ) /cos(θ) ) * ( cos(θ) /sin(θ) )

= 1

larisa [96]3 years ago
4 0
Sec = 1/cos
cot = cos/sin

sec*sin*cot = (1/cos)*sin*(cos/sin) = (sin/cos)*(cos/sin) = 1
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