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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

sec (1) - sec (1) sin (1^{2}) = 0.29340 \dots

sec (1) - sec (1) sin (1^{2})

Refine to a decimal form

= 0.29340 \dots

cos (1^{2}) = 0.54030 \dots

cos (1^{2})

Refine to a decimal form

= 0.54030 \dots

The two sides are not equal

\Rightarrow False

p ro v e (1 + cot^{2} (x)) = \frac{1}{sin ^{2} ( x )}

p ro v e sin (x) (1 + csc (x)) = 1 + sin (x)

p ro v e (sec^{2} (θ) - 1) (sin^{2} (θ) - 1) = - sin^{2} (θ)

p ro v e csc (θ) = \frac{tan ( θ ) cot ( θ )}{sin ( θ )}

p ro v e cot^{2} (x) - cos^{2} (x) = cot^{2} (x) cot (x)

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