Is sin^2(x)cos(x)sec(x)=1-cos^2(x) ?

The answer to whether sin^2(x)cos(x)sec(x)=1-cos^2(x) is True

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prove sin^2(x)cos(x)sec(x)=1-cos^2(x)

prove

sin^{2} (x) cos (x) sec (x) = 1 - cos^{2} (x)

True

Solution steps

sin^{2} (x) cos (x) sec (x) = 1 - cos^{2} (x)

Manipulating left side

sin^{2} (x) cos (x) sec (x)

Express with sin, cos

cos (x) sec (x) sin^{2} (x)

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

= cos (x) \frac{1}{cos ( x )} sin^{2} (x)

Simplify

cos (x) \frac{1}{cos ( x )} sin^{2} (x) : sin^{2} (x)

cos (x) \frac{1}{cos ( x )} sin^{2} (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot cos ( x ) sin ^{2} ( x )}{cos ( x )}

Cancel the common factor:

cos (x)

= 1 \cdot sin^{2} (x)

Multiply:

1 \cdot sin^{2} (x) = sin^{2} (x)

= sin^{2} (x)

= sin^{2} (x)

= sin^{2} (x)

Rewrite using trig identities

sin^{2} (x)

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

sin^{2} (x) = 1 - cos^{2} (x)

= 1 - cos^{2} (x)

= 1 - cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

Is sin^2(x)cos(x)sec(x)=1-cos^2(x) ?
The answer to whether sin^2(x)cos(x)sec(x)=1-cos^2(x) is True