1/tanx-secx+1/tanx+secx=2tanx?

Answer 1

I assume you mean
1/(tanx-secx)+1/(tanx+secx) = 2 tanx

LHS
= 1/(tanx-secx)+1/(tanx+secx)
= (tanx + secx + tanx - secx) / [(tanx)^2- (secx)^2]
= 2tanx / (-1)
= - 2tanx

RHS = 2tanx is not correct.

Answer 2

I assume you mean "Prove the identity." And further that you meant to put on parentheses as shown below.

1/(tanx - secx) + 1/(tanx + secx) = 2tanx
_________

Left Hand Side = 1/(tanx - secx) + 1/(tanx + secx)

= (tanx + secx) / [(tanx - secx)(tanx + secx)]
+ (tanx - secx) / [(tanx + secx)(tanx - secx)]

= (tanx + secx) / (tan²x - sec²x) + (tanx - secx) / (tan²x - sec²x)

= (tanx + secx + tanx - secx) / (-1)

= 2tanx / (-1) = -2tanx

This is NOT an identity.

Answer 3

(a million/tanx+secx)+(a million/tanx-secx) Take LCM and we get [(tan x - sec x ) + ( tan x + sec x) ] / [ tan x +sec x) ( tan x sec x)] Numerator will become 2 tan x denominator will become tan^2 x - sec^2 x = -a million | using relation a million + tan^2 x = sec^2 x so we get 2tan x / -a million -2tan x =RHS