Question

find the value of 8secsquare teta -8 tan square teta. ​

Answer 1

$\large\underline{\sf{Given \:Question - }}$

$\sf \: Find \: the \: value \: of \: 8 {sec}^{2} \theta \: - 8 {tan}^{2} \theta$

$\large\underline{\sf{Solution-}}$

We know that,

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

Thus,

Given expression is

$\rm :\longmapsto\:8 {sec}^{2} \theta \: - 8 {tan}^{2} \theta$

$= \: \sf \: 8 ({sec}^{2} \theta \: - {tan}^{2} \theta)$

$= \: \sf \: 8 \times 1$

$= \: \sf \: 8$

$\rm :\implies\:\boxed{ \bf{8 {sec}^{2} \theta \: - 8 {tan}^{2} \theta = 8}}$

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