Question

sin theta =b then find tan theta +cot theta

Answer 1

sinФ=b

tanФ+cotФ=sinФ/cosФ+cosФ/sinФ

tanФ+cotФ=b/cosФ+cosФ/b

tanФ+cotФ=(b^2+(cosФ)^2)/bcosФ

we know that (cosФ)^2+(sinФ)^2=1,so (cosФ)=1-(sinФ)^2=1-b^2

cosФ=√(1-b^2),put cosФ into equation (b^2+(cosФ)^2)/bcosФ

tanФ+cotФ=(b^2+(cosФ)^2)/bcosФ

tanФ+cotФ=(b^2+(1-b^2)/b(√(1-(b^2))

tanФ+cotФ=1/b(√1-(b^2))