Question

. If SecA + TanA = 5, then SecA - TanA​

Answer 1

Answer:

Question :-

• If secA + tanA = 5, then secA - tanA =

Answer

Given :-

• secA + tanA = 5

To find :-

• secA - tanA

Identity used:-

• sec²θ - tan²θ = 1

Solution :-

secA + tanA = 5

We know, sec²A - tan²A = 1

$\bf\implies \:(secA + tanA )(secA - tanA ) = 1$

$\bf\implies \:5 \times (secA - tanA ) = 1$

$\bf\implies \:secA - tanA = \dfrac{1}{5}$_____________________________________________

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