Question

-. If Sec +tan =1/2 then find the value of sec -tan e?​

Answer 1

Appropriate Question

If secx + tanx = 1/2, find the value of secx - tanx.

Solution :-

Given :-

$\rm :\longmapsto\:secx \: + \: tanx \: = \: \dfrac{1}{2}$

To Find :-

$\rm :\longmapsto\:secx - tanx$

Calculations :-

It is given that

$\rm :\longmapsto\:secx + tanx = \dfrac{1}{2} - - - (1)$

We know,

$\rm :\longmapsto\: {sec}^{2}x - {tan}^{2}x = 1$

$\rm :\longmapsto\:(secx + tanx)(secx - tanx) = 1$

$\: \: \: \: \: \: \: \: \: \red{\bigg \{ \tt \because \: {x}^{2} - {y}^{2} = (x + y)(x - y)\bigg \}}$

$\rm :\longmapsto\:\dfrac{1}{2}(secx - tanx) = 1$

$\bf\implies \:secx - tanx = 2$

Additional Information:-

Relationship between sides and T ratios

sin θ = Opposite Side/Hypotenuse

cos θ = Adjacent Side/Hypotenuse

tan θ = Opposite Side/Adjacent Side

sec θ = Hypotenuse/Adjacent Side

cosec θ = Hypotenuse/Opposite Side

cot θ = Adjacent Side/Opposite Side

Reciprocal Identities

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ

Co-function Identities

sin (90°−x) = cos x

cos (90°−x) = sin x

tan (90°−x) = cot x

cot (90°−x) = tan x

sec (90°−x) = cosec x

cosec (90°−x) = sec x

Fundamental Trigonometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

cosec²θ - cot²θ = 1