Question

If sec theta+tan theta= k then find the value of sin theta in terms of k

Answer 1

let theta = $

sec$ + tan$ = k------------------(1)
we know ,

sec^2$ - tan^2$ = 1

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

hence 

sec$-tan$ = 1/k -----------------(2)
now equation (1)and (2)

2sec$ = k+1/k=(k^2+1)/k

sec$ = (k^2+1)/2k

hence,

cos$ = 2k/(1+k^2)
hence

sin$ = (1-k^2)/(1+k^2)

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Answer 2

hope it is helpful for you please mark it as a friend list the explanation of the answer is in picture and the cos theta equal to 2 k divide by 1 + K square and sin theta equal to 1 minus K square divide by 1 + K square if you have doubt in any question so please Aas hope this answer is correct please follow me four more answer hope these steps are are sufficient to understand this question if any doubt so please comment on the comment section I will explain by second method thank you please mark it as a brain list