Question

secx-tanx=x find sinx cosx tanx ​

Answer 1

Answer:

cos x = 2x/x^2+1

sin x = x^2 -1/ x^2+1

tan x = x^2-1 /2x

Step-by-step explanation:

• sec x + tan x = x (eq no 1)

we know sec x= 1/cos x,

tan x = sinx / cos x

substitute in equation no 1,

1/cos x + sinx /cosx = x

• 1+sinx / cosx = x (eq no 2)

we know sec^2 x - tan^2 x = 1 (or)

(sec x + tan x) ( sec x - tan x) = 1

substituting equation no 1,

x ( sec x - tan x) = 1

• sec x - tan x = 1/x ( eq no 3)

Solving this using formula,

1/cos x - sin x/ cos x = 1/x

• 1-sin x / cos x = 1/x (eq no 4)

now Adding eq 2 & 4,

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

2/ cos x = x^2 + 1/ x

• cos x = 2x / x^2 +1

subtracting eq 1 & 3,

(sec x + tan x) - ( sec x - tan x) = x - 1/x

sec x + tan x - sec x + tan x = x^2 -1 / x

2 tan x = x^2 -1/ x

• tan x = x^2 -1/ 2x

Finally we know sin x = tan x . cos x,

substitute tan & cos x,

sin x = tan x. cos x

= (x^2 -1/ 2x) . ( 2x/ x^2 +1)

• sin x = x^2 -1 / x^2 + 1

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