Question

Tan square theta multiplied by cot square theta is 1

Answer 1

Answer:

tan^2 theta ×cot^2 theta = 1

proof

we know

tan × cot =1

tan × 1/ tan = 1

therefore

tan^2 × cot^2=1

tan^2 ×1/tan^2 = 1

hence proved

Answer 2

Answer:

To Prove :

{(tan)^2 theta } × {(cot)^2 theta} = 1

Proof :

We know that,

tan theta = sin theta / cos theta

cot theta = cos theta / sin theta

So, by applying the values in L.H.S. :

{(tan)^2 theta} × {(cot)^2 theta} =

= {(sin theta / cos theta)^2} ×

{( cos theta / sin theta)^2}

= { sin^2 theta / cos^2 theta } ×

{ cos^2 theta / sin^2 theta }

= { sin^2 theta / cos^2 theta ×

cos^2 theta / sin^2 theta }

= 1 = R.H.S.

L.H.S = R.H.S

Hence proved.