if cottheta=7/8 then what is the value of 1+costheta/1-sintheta*1-costheta/1+sintheta.

Answer 1

tan T = 8/7 = sin T/cos T

8 cos T = 7 sin T
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(1+cos T)(1-cosT)
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(1-sin T) (1+sin T)

that is easy

1 - cos^2 T
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(1 - sin^2 T)

but

1-cos^2 = sin^2 and 1 - sin^2 = cos ^2

so

sin^2 T/cos^2 T = tan^2 T = 8^2/7^2 = 64/49