Is sec(x)-tan(x)*sin(x)= 1/(sec(x)) ?

The answer to whether sec(x)-tan(x)*sin(x)= 1/(sec(x)) is True

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prove sec(x)-tan(x)*sin(x)= 1/(sec(x))

prove

sec (x) - tan (x) \cdot sin (x) = \frac{1}{sec ( x )}

True

Solution steps

sec (x) - tan (x) sin (x) = \frac{1}{sec ( x )}

Manipulating left side

sec (x) - tan (x) sin (x)

Express with sin, cos

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

Rewrite using trig identities

= cos (x)

Use the basic trigonometric identity:

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{( 1 + cos ( 2 y ) )}{sin ^{2} ( y )} = 2 cot^{2} (y)

4 cos^{2} (B) - 4 sin^{2} (B) = 4 - 8 sin^{2} (B)

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

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

cos (4 A) = 8 cos^{4} (A) - 8 cos^{2} (A) + 1

Is sec(x)-tan(x)*sin(x)= 1/(sec(x)) ?
The answer to whether sec(x)-tan(x)*sin(x)= 1/(sec(x)) is True