Question

(cosec A-sinA) (secA-cosA)=1/tanA+cotA

Answer 1

We know, cosec A = 1/sinA

and sec A = 1/cos A

Substituting these value in LHS,

LHS = (1/sinA - sinA) (1/cosA - cosA)

LHS = 1/sinA (1-sin^2 A) 1/cos A (1-cos^2 A)

Also, 1-sin^2 A = cos^2 A

and, 1-cos^2 A = sin^2 A

LHS = (cos^2 A/ sinA)(sin^2 A/ cos A)

By cancellation of comman factors,

LHS = cos A * sin A

Now, solving RHS

RHS = 1/tanA+cotA

tanA = sinA/cosA and cotA = cosA /sin A

On solving,

RHS = 1/sin^2 A+cos^2 A/cosA*sinA

sin^2 A + cos^2 A = 1

RHS = cosA*sinA

LHS = RHS