Question

please tell me this answer
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Answer 1

Answer:

which class question it was???

Answer 2

Answer:

sec theta - tan theta = K --------(1)

=> sec theta - K = tan theta --------- (3)

since,

sec² theta - tan²theta = 1

=> (sec theta + tan theta) (sec theta - tan theta) = 1

=> (sec theta + tan theta)* K = 1

=> (sec theta + tan theta) = 1/K ---------(2)

On additing equation 1 and 2, we get,

2 sec theta = K + 1/K

=> sec theta = (K² + 1)/2K

Since, tan theta = sin theta / cos theta

=> tan theta = sin theta * sec theta

{ since, 1/cos theta = sec theta}

=> sin theta * sec theta = sec theta - K

{from equation 3}

=> sin theta = (sec theta - K) / sec theta

=> sin theta = 1 - (K/sec theta)

=> sin theta = 1 - (K * 2K/ K²+1)

=> sin theta = 1 - (2K²/ K²+1)

=> sin theta = (K² +1 - 2K²)/ (1+K²)

=> sin theta = (1- K²) /(K² +1)

=> (K²+1) sin theta = -(K²-1)