What is expand (sec(θ)-tan(θ))(sec(θ)+tan(θ))^2 ?

The solution to expand (sec(θ)-tan(θ))(sec(θ)+tan(θ))^2 is sec(θ)+tan(θ)

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expand (sec(θ)-tan(θ))(sec(θ)+tan(θ))^2

expand

(sec (θ) - tan (θ)) (sec (θ) + tan (θ))^{2}

sec (θ) + tan (θ)

Solution steps

(sec (θ) - tan (θ)) (sec (θ) + tan (θ))^{2}

= (sec (θ) + tan (θ))^{2} (sec (θ) - tan (θ))

Expand

(sec (θ) + tan (θ))^{2} : sec^{2} (θ) + 2 sec (θ) tan (θ) + tan^{2} (θ)

= (sec^{2} (θ) + 2 sec (θ) tan (θ) + tan^{2} (θ)) (sec (θ) - tan (θ))

Distribute parentheses

= sec^{2} (θ) sec (θ) + sec^{2} (θ) (- tan (θ)) + 2 sec (θ) tan (θ) sec (θ) + 2 sec (θ) tan (θ) (- tan (θ)) + tan^{2} (θ) sec (θ) + tan^{2} (θ) (- tan (θ))

Simplify

sec^{2} (θ) sec (θ) + sec^{2} (θ) (- tan (θ)) + 2 sec (θ) tan (θ) sec (θ) + 2 sec (θ) tan (θ) (- tan (θ)) + tan^{2} (θ) sec (θ) + tan^{2} (θ) (- tan (θ)) : sec (θ) + tan (θ)

= sec (θ) + tan (θ)

(x^{2} + y^{2}) e^{- x^{2} - y^{2}}

x^{\frac{1}{3}} (x^{\frac{2}{3}} - x)

\frac{( 50 s )}{( s + 10 ) ( s + 1 )}

sin (\frac{1}{2} (x + \frac{π}{4}))

4 (a cos (2 x) + b sin (2 x))

What is expand (sec(θ)-tan(θ))(sec(θ)+tan(θ))^2 ?
The solution to expand (sec(θ)-tan(θ))(sec(θ)+tan(θ))^2 is sec(θ)+tan(θ)