Question

1 + cot2 30 =cosec2
​

Answer 1

Step-by-step explanation:

L.H.S= 1+cot^2(30)

= 1+(cot30)^2

= 1+(cos30/sin30)^2

= 1+(cos30÷sin30)^2

= 1+(√3/2÷ 1/2)^2

= 1+(√3/2× 2/1)^2

= 1+(2√3/2)^2

= 1+(√3)^2

= 1+3

=4

R.H.S= Cosec^2(30)

=(cosec30)^2

=(1/sin30)^2

=(1÷sin30)^2

=(1÷1/2)^2

=(1×2/1)^2

=(2)^2

=4

Thus, L.H.S= R.H.S. i.e. 1+cot^2(30)=

Cosec^2(30) [proved