Question

if secQ= 5/4 how that ( 2cos - sinQ/cotQ-tanQ) = 12/7

Answer 1

secQ=5/4

Proceeding in solving the equation we get,
=cosQ=4/5  [.·. cosQ=1/secQ]
Now finding the value of sinQ,
⇒sin²Q+cos²Q=1
⇒sin²Q=√1-cos²Q
           =√1-(4/5)²
           =√1-(16/25)
           =√(25-16)/25
           =√9/25
           =3/5
hence value of sinQ=3/5

Now finding the value of cotQ,
cotQ=cosQ/sinQ
       =(4/5)/(3/5)
       =4/3
hence value of cotQ=4/3

Now finding the value of tanQ,
tanQ=3/4 [.·. tanQ=1/cotQ]

Now putting all the values in the above equation,
We get,
⇒2cosQ-sinQ/cotQ-tanQ⇒2.(4/5)-(3/5)/(4/3)-(3/4)
⇒(8/5)-(3/5)/(16-9)/12
⇒(5/5)/(7/12)
⇒12/7

Hence, proved.

Answer 2

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