Question

if seco+Tan o =p show that.
Coseco=p2+1/p2-1​

Answer 1

Answer:

sec@ + tan@ = p

=> 1/(sec@+tan@) = 1/p

=> (sec@-tan@)/(sec²@-tan²@) = 1/p

=> sec@ - tan@ = 1/p

=> (sec@+tan@)+(sec@-tan@) = p+1/p

=> 2sec@ = p+1/p

=> sec@ = (p²+1)/2p

=>cos@ = 2p/(p²+1)

=> cos²@ = 4p²/(p²+1)²

=> 1-sin²@ = 4p²/(p²+1)²

=> sin²@ = 1-4p²/(p²+1)²

=> sin²@ = (p^4+2p²+1-4p²)/(p²+1)²

=> sin²@ = (p^4 - 2p² + 1)/(p²+1)²

=> sin²@ = (p²-1)²/(p²+1)²

=> sin@ = (p²-1)/(p²+1)

=> cosec@ = (p²+1)/(p²-1)