How do you prove $(sin x + cos x) (tan x + cot x) = sec x + csc x$ $(sinx+cosx)(Tanx+cotx)=secx+cscx$ ?

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How do you prove $(sin x + cos x) (tan x + cot x) = sec x + csc x$ $(sinx+cosx)(Tanx+cotx)=secx+cscx$ ?

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Answer 1 · 2018-03-22T04:42:59

We have:

$(sin x + cos x) (\frac{sin x}{cos x} + \frac{cos x}{sin x}) = sec x + csc x$ $(sinx + cosx)(sinx/cosx + cosx/sinx) = secx +cscx$

$(sin x + cos x) (\frac{{sin}^{2} x + {cos}^{2} x}{sin x cos x}) = sec x + csc x$ $(sinx + cosx)((sin^2x + cos^2x)/(sinxcosx)) = secx + cscx$

$\frac{sin x + cos x}{sin x cos x} = sec x + csc x$ $(sinx +cosx)/(sinxcosx) = secx + cscx$

$\frac{sin x}{sin x cos x} + \frac{cos x}{sin x cos x} = sec x + csc x$ $sinx/(sinxcosx) + cosx/(sinxcosx) = secx + cscx$

$\frac{1}{cos x} + \frac{1}{sin x} = sec x + csc x$ $1/cosx + 1/sinx = secx + cscx$

$sec x + csc x = sec x + csc x$ $secx + cscx = secx + cscx$

$L H S = R H S$ $LHS = RHS$

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How do you prove $(sin x + cos x) (tan x + cot x) = sec x + csc x$ $(sinx+cosx)(Tanx+cotx)=secx+cscx$ ?

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How do you prove (sinx+cosx)(tanx+cotx)=secx+cscx(sinx+cosx)(Tanx+cotx)=secx+cscx?

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How do you prove $(sin x + cos x) (tan x + cot x) = sec x + csc x$ $(sinx+cosx)(Tanx+cotx)=secx+cscx$ ?