Question

If sec theeta+tan theeta=k, then prove that sin theeta=k²-1/k²+1

Answer 1

Answer:

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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