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

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

Popular >

prove 1/(1-sin(x))=(1+sin(x))/(cos^2(x))

prove

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

True

Solution steps

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

Manipulating left side

\frac{1}{1 - sin ( x )}

Rewrite using trig identities

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

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (x) \cdot cos^{2} (x) = 1 - cos^{2} (x)

sin^{2} (A) - sin^{2} (A) cos^{2} (A) = sin^{4} (A)

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

cot^{2} (x) + csc^{2} (x) = 1 + 2 cot^{2} (x)

sin (a) sec (a) tan (a) + 1 = sec^{2} (a)

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