Question

If (1+cosA )( 1-cosA) = 3/4, find the value of secA.​

Answer 1

$\tt{Solution:-}$

$\tt{Step \:by \:step \:explanation:-}$

$\large\tt{Given:-}$

$\large\tt( 1 + cosA ) ( 1 - cosA ) = \tt\dfrac{3}{4}$

$\large\tt{To find:-}$

$\tt{secA}$

$\large\tt{Solution:-}$

$\large\tt( 1 + cosA ) ( 1 - cosA ) = \tt\dfrac{3}{4}$

$\large\tt{It\: is\: in\: form \:of (a + b) ( a - b ) = a^2-b^2}$

Similarily,

$\large\tt( 1 + cosA ) ( 1 - cosA ) = \tt\dfrac{3}{4}$

$\large\tt{1 - cos^2A =} \tt\dfrac{3}{4}$

$\large\tt{From,\: \: Trigonmetric \: \: Identities}$

$\large\tt{sin^2A + cos^2A = 1 }$

$\large\tt{1- cos^2A = sin²A}$

So,

$\large\tt{1 - cos^2A} = \tt\dfrac{3}{4}$

$\large\tt{sin^2A}= \tt\dfrac{3}{4}$

$\large\tt{sinA}= \tt\sqrt{3}{4}$

$\large\tt{sinA} = \tt\sqrt{3}$/2

$\large\tt{From\: \: Trigonmetric\: \: table}$

$\large\tt{sin60} = \tt\sqrt{3}$/2

So,

$\large\tt{sinA} = \tt\sqrt{3}$/2

A = 60°

Now,

$\large\tt{secA = sec60}$

$\large\tt{secA = 2}$

$\large\tt{So\: secA=2}$

__________________

$\large\tt{Know\: more:-}$

$\large\tt{Trigonmetric\: \: Identities:-}$

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

$\large\tt{Trigonmetric \: \:relations:-}$

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

$\large\tt{Trigonmetric \: \:ratios:-}$

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj

Answer 2

Answer:

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