Question

Prove that: Secx-Cosx/ tanx= Sinx

Answer 1

Hello from MrBillDoesMath

Answer:

See below

Discussion:

Be definition secx = (1/cos)\ and tanx = sinx/cos. Substitute these in the the original equation

(secx - cosx)/tanx = ( (1/cosx ) -cosx) )/ (sinx/cosx) ) =

Multiply top and bottom by cosx:

cosx ( (1/cosx) - cosx) / ( ( sinx /cosx) * cosx ) =

(1 - (cosx)^2) / sinx

From (sinx)^2 + (cosx)^2 -1, 1 - (cosx) ^2 = (sinx)^2. Substitute this in the above equation to get

(sinx)^2 / (sinx) = sinx

Thank you,

Mr. B