How do you simplify $(tanx)/(1+secx) + (1+secx)/tanx = 2cscx$ ?

Question

22598 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-20T12:05:10

$LHS=(tanx)/(1+secx) + (1+secx)/tanx$

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

$=(tanx(secx-1))/(sec^2x-1)+ (1+secx)/tanx$

$=(tanx(secx-1))/tan^2x+ (1+secx)/tanx$

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

$=secx/tanx-1/tanx+ 1/tanx+secx/tanx$

$=(2secx)/tanx$

$=(2/cosx)/(sinx/cosx)$

$=2/sinx$

$= 2cscx=RHS$

How do you simplify (tanx)/(1+secx) + (1+secx)/tanx = 2cscx(tanx)/(1+secx) + (1+secx)/tanx = 2cscx?