Question

if cos theta is equal to 2t by 1 plus t square find cosec theta and cot theta
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Answer 1

as I let theta equal to r

then cos(r) =2t/(1+t^2)

if

we put t=tan(u)

then I know that cos(2r)= 2tan(r)/(1+(tan(r)^2)

so

cos(r)=2tan(u)/(1+(tan)^2))

then

we see this carefully the we find that

cos(r)=cos(2u)

r=2u

mean

theta equal to r and r equal to 2u

so and you know cos(r) =cos (2u)

then by triangle law cos(r) =base / hypotenuse

base=cos(2u) and hypotenuse=1

then

cosec(r) =1/(1+cos(2u)^2)

cot(r) =(1+cos(2u)^2)/cos(2u)

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