Question

(cosecQ-sinQ) (secQ-cosQ) =1 ÷tanQ-cotQ​

Answer 1

Answer:

(cosecQ - sinQ) (secQ - cosQ) =1 ÷ ( tanQ + cotQ​ )

Step-by-step explanation:

To prove : (cosecQ - sinQ) (secQ - cosQ) =1 ÷ ( tanQ + cotQ​ )  (pls change the sign in your question)

LHS = (cosecQ - sinQ) (secQ - cosQ)

        = ($\frac{1}{sinQ}$ - sinQ) ($\frac{1}{cosQ}$ - cosQ)

        = ($\frac{1-sin^2Q}{sinQ}$ ) ($\frac{1-cos^2Q}{cosQ}$)

        = ($\frac{cos^2Q}{sinQ}$ ) ($\frac{sin^2Q}{cosQ}$)

        = ($\frac{cos^2Q}{sinQ}$ ) ($\frac{sin^2Q}{cosQ}$)

        = sinQ.cosQ

        = (sinQ.cosQ) / 1

        = sinQ.cosQ / (sin²Q+cos²Q)

        = 1 / ($\frac{sin^2Q+cos^2Q}{sinQ.cosQ}$)

        = 1 / ($\frac{sin^2Q}{sinQ.cosQ} + \frac{cos^2Q}{sinQ.cosQ}$)

        = 1 / ($\frac{sinQ}{cosQ} + \frac{cosQ}{sinQ}$)

        = 1 / (tanQ+cotQ)

        = RHS

=> LHS = RHS

Hence proved