Kel asked in Science & MathematicsMathematics · 1 decade ago

simplify: (( tan x) / ( csc x + cot x))?

a. sec x - 1

b. sec x + 1

c. tan x csc x + tan x cot x

d. 1 - (1/ cos x)

e. none of these here

2 Answers

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  • 1 decade ago
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    becuase csc^2 x -c cot^2 x = 1 multiply both num and den by csc x - cot x

    = tan x(csec x - cot x)

    = tan x csc x - 1

    = sinx / cos x * 1/ sin x -1

    = sec x -1

    so ans is a

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  • 1 decade ago

    (tan(x))/(csc(x) + cot(x))

    (sin(x)/cos(x))/((1/sin(x)) + (cos(x)/sin(x)))

    (sin(x)/cos(x))/((1 + cos(x))/sin(x))

    (sin(x)/cos(x))*(sin(x)/(1 + cos(x)))

    (sin(x)^2)/(cos(x)(1 + cos(x)))

    (1 - cos(x)^2)/(cos(x)(1 + cos(x)))

    ((1 - cos(x)(1 + cos(x)))/(cos(x)(1 + cos(x)))

    (1 - cos(x))/(cos(x))

    (1/cos(x)) - (cos(x)/cos(x))

    sec(x) - 1

    ANS : A.) sec(x) - 1

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