Math, asked by vinaypal53826, 2 months ago

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

Answers

Answered by ravi2303kumar
0

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

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