Question

prove that secant theta X cosecant theta = tan theta + cot theta

Answer 1

sec(θ) = 1/cos(θ)

cosec(θ) = 1/sin(θ)

therefore sec(θ)*cosec(θ) = 1/sin(θ)*cos(θ) --> Eqution 1

Now tan(θ) + cot(θ) =

sin(θ)/cos(θ) + cos(θ)/sin(θ)

= (sin²(θ) + cos²(θ) )/ sin(θ)*cos(θ) --> Equation 2

Now you know that sin²∅ + cos²∅ = 1

hence rquation 2 = equation 1

Answer 2

hii
here is ir answer...

we know that sec theta =1/cos theta

cosec theta=1/ sin theta

now
sec theta.cosec theta=1/sin theta.cos theta....................... (1)

again tan theta+cot theta=

sin^2theta+cos^2theta/sin theta.cos theta

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

eq..1=eq.2
L.H.S=R.H.S