If tan theta = 12/5, then find the value of 1+sin theta/ 1- sin theta

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Solution

Hi ,

Here I am using A instead of theta.

tanA = 12/5

CotA = 5/12

Cosec² A = 1 + cot² A

= 1 + ( 5/12 )²

= 1 + 25/144

= ( 144 + 25 ) / 144

= 169 / 144

cosecA = √ ( 13/12 )²

1/sinA = 13/12

Therefore ,

SinA = 12/13
1+sin A/1-sinA=(1+12/13)/(1-12/13)
=(25/13)/(1/13)
=25

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