Question

If TanA=CotA then find CosA with more explanation​

Answer 1

Answer:

Question:-

• If tanA = cotA, find cosA.

$\bf\underbrace\orange{Answer:}$

Given :-

• tanA = cotA

To find :-

• The value of cosA.

Formula used :-

• sec²θ - tan²θ = 1
• cot θ = 1/tan θ

Solution:-

$\bf \:tanA = cotA$

$\bf\implies \:tanA = \dfrac{1}{tanA}$

$\bf\implies \: {tan}^{2} A = 1$

$\bf\implies \: {sec}^{2} A - 1 = 1$

$\bf\implies \: {sec}^{2} A = 2$

$\bf\implies \:secA = \sqrt{2}$

$\bf\implies \:cosA = \dfrac{1}{ \sqrt{2} }$

_____________________________________________

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

_____________________________________________