Is 1/((sec(θ))^2)+1/((csc(θ))^2)=1 ?

The answer to whether 1/((sec(θ))^2)+1/((csc(θ))^2)=1 is True

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prove 1/((sec(θ))^2)+1/((csc(θ))^2)=1

prove

\frac{1}{( sec ( θ ) ) ^{2}} + \frac{1}{( csc ( θ ) ) ^{2}} = 1

True

Solution steps

\frac{1}{( sec ( θ ) ) ^{2}} + \frac{1}{( csc ( θ ) ) ^{2}} = 1

Manipulating left side

\frac{1}{( sec ( θ ) ) ^{2}} + \frac{1}{( csc ( θ ) ) ^{2}}

Simplify

= \frac{1}{sec ^{2} ( θ )} + \frac{1}{csc ^{2} ( θ )}

Express with sin, cos

= cos^{2} (θ) + sin^{2} (θ)

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

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

tan (x) - tan (x) sin (x) = cos (x) sin (x)

cot (x) + tan (x) = sec (csc (x))

cos (\frac{1}{3} π) = cos (- \frac{1}{3} π)

7 sec (θ) = - 9.2

Is 1/((sec(θ))^2)+1/((csc(θ))^2)=1 ?
The answer to whether 1/((sec(θ))^2)+1/((csc(θ))^2)=1 is True