Question

If tan theta+1/tan theta = 2 then value of cosec theta is

Answer 1

Answer:

tan theta+1/tan theta=2

1/cot theta + cot theta*=2

(1+cot^2 theta)/cot theta=2

cosec^2 theta/cot theta=2

(1/sin^2theta)/(cos theta/sin theta)=2

(1/sin theta)/(cos theta)=2

2sintheta.costhta=1

sin 2 theta=1=sin 90

2theta=90

theta=90/2=45

cosec theta=cosec 45=√2

Answer 2

Answer:

cosecθ = cosec45 degree = $\sqrt2$

Step-by-step explanation:

tanθ + 1/tanθ = 2

=>1/cotθ + cotθ = 2

=>(1 + cot²θ)/cotθ = 2

=>cosec²θ/cotθ=2

=>1/sin²θ × sinθ/cosθ=2

=>1/sinθ*cosθ=2

=>2sinθcosθ=1

=>sin2θ=sin90

=>2θ=90

=>θ=45 degree

so,

cosec 45 degree = $\sqrt2$