What is sin(x)(1+cot(x))+cos(x)(1-tan(x)) ?

The solution to sin(x)(1+cot(x))+cos(x)(1-tan(x)) is 2cos(x)

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simplify sin(x)(1+cot(x))+cos(x)(1-tan(x))

simplify

sin (x) (1 + cot (x)) + cos (x) (1 - tan (x))

2 cos (x)

Solution steps

sin (x) (1 + cot (x)) + cos (x) (1 - tan (x))

Expand

sin (x) (1 + cot (x)) : cos (x) + sin (x)

= cos (x) + sin (x) + cos (x) (1 - tan (x))

Expand

cos (x) (1 - tan (x)) : cos (x) - sin (x)

= cos (x) + sin (x) + cos (x) - sin (x)

Group like terms

= cos (x) + cos (x) + sin (x) - sin (x)

Add similar elements:

cos (x) + cos (x) = 2 cos (x)

= 2 cos (x) + sin (x) - sin (x)

Add similar elements:

sin (x) - sin (x) = 0

= 2 cos (x)

(r cos (θ)) (r sin (θ))

x^{4} - x^{3} - 5 x^{2} - x - 6

\frac{\frac{4 p - 4}{p}}{\frac{9 p - 9}{4 p ^{2}}}

\frac{2 x ^{- 1} - 3 x ^{- 2}}{4 x ^{- 3}}

(2 x - 5)^{4}

What is sin(x)(1+cot(x))+cos(x)(1-tan(x)) ?
The solution to sin(x)(1+cot(x))+cos(x)(1-tan(x)) is 2cos(x)