Question

if sec beta +tan beta=p, then find the value of sin beta in terms of p​

Answer 1

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let theta =@

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

we know ,

sec^2@-tan^2@=1

(sec@-tan@)(sec@+tan@)=1

hence ,

sec@-tan@=1/p -----------------(2)

now equation (1)and (2)

2sec@=p+1/p=(p^2+1)/p

sec@=(p^2+1)/2p

hence,

cos@=2p/(1+p^2)

hence ,

sin@=(1-p^2)/(1+p^2)

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Answer 2

Answer:

let theta =@

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

we know ,

sec^2@-tan^2@=1

(sec@-tan@)(sec@+tan@)=1

hence ,

sec@-tan@=1/p -----------------(2)

now equation (1)and (2)

2sec@=p+1/p=(p^2+1)/p

sec@=(p^2+1)/2p

hence,

cos@=2p/(1+p^2)

hence ,

sin@=(1-p^2)/(1+p^2)