How do you verify $\frac{{(sec x - tan x)}^{2} + 1}{(sec x csc x) - (tan x csc x)} = 2 tan x$ $((sec x - tan x)^2 + 1)/((sec x csc x) - (tan x csc x)) = 2tan x$ ?

Question

How do you verify $\frac{{(sec x - tan x)}^{2} + 1}{(sec x csc x) - (tan x csc x)} = 2 tan x$ $((sec x - tan x)^2 + 1)/((sec x csc x) - (tan x csc x)) = 2tan x$ ?

1 Answer

Impact of this question

8677 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-07T08:51:24

$L H S = \frac{{(sec x - tan x)}^{2} + 1}{sec x csc x - tan x csc x}$ $LHS=((secx-tanx)^2+1)/(secxcscx-tanxcscx)$

$= \frac{{(\frac{1}{cos x} - \frac{sin x}{cos x})}^{2} + 1}{sec x csc x - sin x sec x csc x}$ $=((1/cosx-sinx/cosx)^2+1)/(secxcscx-sinxsecxcscx)$

$= \frac{(\frac{{(1 - sin x)}^{2}}{{cos}^{2} x}) + 1}{sec x csc x (1 - sin x)}$ $=(((1-sinx)^2/cos^2x)+1)/(secxcscx(1-sinx))$

$= \frac{\frac{1 - 2 sin x + {sin}^{2} x + {cos}^{2} x}{{cos}^{2} x}}{sec x csc x (1 - sin x)}$ $=((1-2sinx+sin^2x+cos^2x)/cos^2x)/(secxcscx(1-sinx))$

$= \frac{\frac{1 - 2 sin x + 1}{{cos}^{2} x}}{sec x csc x (1 - sin x)}$ $=((1-2sinx+1)/cos^2x)/(secxcscx(1-sinx))$

$= \frac{\frac{2 - 2 sin x}{{cos}^{2} x}}{sec x csc x (1 - sin x)}$ $=((2-2sinx)/cos^2x)/(secxcscx(1-sinx))$

$=(2cancel((1-sinx)))/(cos^2xsecxcscxcancel((1-sinx)))$

$=2/(cosx*1/sinx)$

$=(2sinx)/cosx$

$=2tanx=RHS$

Proved

Science

Math

Humanities

... and beyond

How do you verify $\frac{{(sec x - tan x)}^{2} + 1}{(sec x csc x) - (tan x csc x)} = 2 tan x$ $((sec x - tan x)^2 + 1)/((sec x csc x) - (tan x csc x)) = 2tan x$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you verify ((sec x - tan x)^2 + 1)/((sec x csc x) - (tan x csc x)) = 2tan x(secx−tanx)2+1(secxcscx)−(tanxcscx)=2tanx((sec x - tan x)^2 + 1)/((sec x csc x) - (tan x csc x)) = 2tan x?

1 Answer

Related questions

Impact of this question

How do you verify $\frac{{(sec x - tan x)}^{2} + 1}{(sec x csc x) - (tan x csc x)} = 2 tan x$ $((sec x - tan x)^2 + 1)/((sec x csc x) - (tan x csc x)) = 2tan x$ ?