Question

Prove lhs = rhs: sec2theta +cosec2theta =sec2theta×cosec2theta

Answer 1

Trigonometry

First of all let 'e' instead of theta

Now
We have
sec²e +cosec²e =sec²e×cosec²e

Have to prove LHS = RHS

LHS = sec²e +cosec²e
= (1/cos²e)+(1/sin²e). [As sece = 1/cose and cosece = 1/sine]
=(sin²e + cos²e)/(sin²e.cos²e)
= 1/(sin²e.cos²e). [As sin²e + cos²e = 1]
= (1/sin²e) ×(1/cos²e)
= cosec²e×sec²e = RHS

That's it
Hope it helped (ㆁωㆁ*)

Answer 2

LHS=1/cos^2theta+1/sin^2theta
sin^2+cos^2/cos^2sin^2
1/cos^2sin^2. (cos^2+sin^2=1)
1/cos^2×1/sin^2
sec^2theta×cosec^2theta.....
thanks