Question

if tan tita=cos tita then the value of acute angle tita​

Answer 1

$\sf{Answer}$

Iam considering theta = A

Topic :- Trignometry

Appropriate Question :-

If tanA=cosA , then sinA=

Given that :-

tan A = cosA

To find :-

sin A

Formulae Used :-

tan A = $\sf\dfrac{sinA}{cosA}$

cos²A = 1 - sin²A

Range of sinA is ( -1 , 1 )

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Lets do !!!!

tanA=cosA

$\sf\dfrac{sinA}{cosA}$ = cosA

Do cross multiplication

sinA = cos²A

sinA = 1 - sin²A

Tranpose to LHS

sinA -1 + sin²A = 0

sin²A + sinA -1 = 0

Let sinA = x

x² + x - 1 = 0

Solving by using Quadratic formula

$\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$

$\dfrac{-1\pm\sqrt{(1)^2 -4(1)(-1)}}{2(1)}$ = sinA

$\dfrac{-1\pm\sqrt { 1 + 4}}{2}$ = sinA

$\dfrac{-1\pm\sqrt{5}}{2}$ = sinA

sinA = $\sf\dfrac{-1 +\sf\sqrt{5}}{2}$ or

sinA = $\sf\dfrac{-1-\sf\sqrt{5}}{2}$

We have to take only sinA = $\sf\dfrac{-1 +\sf\sqrt{5}}{2}$

Its value is 0.61 So, ATQ range of sin A

sinA = $\sf\dfrac{-1-\sf\sqrt{5}}{2}$ = -1.65 It does not lie in range of sinA

So, sinA = $\sf\dfrac{-1 +\sf\sqrt{5}}{2}$

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know more:-

Trignometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trignometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trignometric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj