(secx/secx-1)=(csc^2)x +cotx cscx?

Question

(secx/secx-1)=(csc^2)x +cotx cscx

how do i prove it with identities

Answer 1

1) Applying NUmerator and denominator of left hand side by (secx + 1)



LHS = [secx(secx + 1)]/(secx - 1)(secx + 1) = secx (secx + 1)/(sec2x - 1)



= secx (secx + 1)/tan²x [Since secNx - 1 = tan²x]



2) Changing, secx = 1/cosx and tan²x = sin²x/cos²x and simplifying the above,



LHS = (1 + cosx)/sin²x = 1/sin²x + cosx/sin²x = csc²(x) + cot(x)*csc(x) = RHS



Thus LHS = RHS [Proved]

Answer 2

LS = (secx/secx-1)

Multiply N and D by (secx+1)

= secx(secx +1)/(sec^2x -1)

= (sec^2x +secx}/tan^2x because sec^2x -1 = tan^2x

= {sec^2x/tan^2x} + (secx/tan^2x)

= cosec^2 x + cotx cosec x ............RS

Hece (secx/secx-1)=(csc^2)x +cotx cscx

Answer 3

(cotx)/(cscx-a million)=(cscx+a million)/(cotx) (cotx)^2 = (cscx -a million)(cscx+a million) (cotx)^2 = (cscx)^2 -a million (cosx)^2/(sinx)^2 = a million/(sinx)^2 - a million (cosx)^2/(sinx)^2 - a million/(sinx)^2 = -a million ((cosx)^2 - a million)/(sinx)^2 = - a million -a million(a million - (cosx)^2) / (sinx)^2 = -a million -a million*(sinx)^2 / (sinx)^2 = -a million -a million = -a million .......................identity!!!!!!!!!...

Answer 4

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