Question

if sec tita is 5 then find the cos tita and tan tita​

Answer 1

Answer:

Question:-

• If secθ = 5, fimd the value of cosθ and tanθ.

Answer :-

Given :-

• secθ = 5

To find :-

• The value of cosθ and tanθ

Identity used :-

$\bf \:cosθ = \dfrac{1}{secθ}$

$\bf \: {sec}^{2} θ - {tan}^{2} θ = 1$

$\large{\boxed{\boxed{\sf{Solution}}}}$

Part 1.

$\bf \:secθ = 5$

$\bf\implies \:cosθ = \dfrac{1}{secθ} = \dfrac{1}{5}$

Part 2.

$\bf \:secθ = 5$

we know

$\bf \:{sec}^{2} θ - {tan}^{2} θ = 1$

$\bf\implies \: {5}^{2} - {tan}^{2} θ = 1$

$\bf\implies \: {tan}^{2} θ = 5 - 1$

$\bf\implies \: {tan}^{2} θ = 4$

$\bf\implies \:tanθ \: = 2$

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Additional Information:-

• 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

The Reciprocal Identities are given as:

• 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