Question

If cosA=
1/2
then find the value of
2secA*sinA/1+tan^2A​

Answer 1

APPROPRIATE QUESTION:-

If cosA = 1/2 Then find the value of 2secA × sinA / 1+ tan²A

SOLUTION:-

cosA = 1/2

But We know cos60° = 1/2

So,

cosA = cos60°

A = 60°

Now,

$\dfrac{2secA \times sinA}{1+tan^2A}$

$\dfrac{2sec60° \times sin60°}{1 + tan^260°}$

• sec 60° = 2
• sin60° = √3/2
• tan60° = √3

Putting down the values

$\dfrac{2 \times 2 \times \frac{ \sqrt{3} }{2} }{1 + \sqrt({3}) {}^{2} }$

$\dfrac{ \dfrac{4 \sqrt{3} }{2} }{1 + 3}$

$\dfrac{2 \sqrt{3} }{4}$

$\dfrac{ \sqrt{3} }{2}$

$\dfrac{2secA \times sinA}{1+tan^2A}= \dfrac{ \sqrt{3} }{2}$

KNOW MORE :-

Trigon metric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trigometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trigonmetric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj