Proof trigonometric identities.\frac{1-\sin(-x)}{\cos x+\cos(-x)\sin x}=\sec x

Jerold

Jerold

Answered question

2021-09-07

Proof trigonometric identities.
1sin(x)cosx+cos(x)sinx=secx

Answer & Explanation

avortarF

avortarF

Skilled2021-09-08Added 113 answers

Given :
1sin(x)cosx+cos(x)sinx=secx
Considering left-hand side 1sin(x)cosx+cos(x)sinx
Using sin(θ)=sinθ and cos(θ)=cosθ,
1sin(x)cosx+cos(x)sinx=1(sin(x))cosx+cos(x)sinx
1sin(x)cosx+cos(x)sinx=1+sin(x)cosx+cos(x)sinx
1sin(x)cosx+cos(x)sinx=1+sin(x)cosx(1+sinx)
1sin(x)cosx+cos(x)sinx=1cosx
Using secθ=1cosθ
1sin(x)cosx+cos(x)sinx=secx
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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