Question

{1+cotx-sec(90+x)}{1+cotx+sec(90+x)}=2cotx prove it​

Answer 1

Step-by-step explanation:

we have to prove, [1+cotx-sec(90+x)][1+cotx+sec(90+x)] =

2cotx

LHS, [(1+cotx)-sec(90+x)][(1+cotx)+sec(90+

x)]

applying identity, (a-b)(a+b) = a²-b²

[(1+cotx)²-sec²(90+x)]

as, sec(90+x) = -cosecx

so, [1+cot²x+2cotx-(-cosecx)²]

[1+cot²x+2cotx-cosec²x]

[cot²x+2cotx-(cosec²x-1)]

as, cosec²x-1 = cot²x {it's identity}

so, [cot²x+2cotx-cot²x]

=> 2cotx = RHS

hence proved....