Question

if sinA=4/5 then tan2A will be??​

Answer 1

Answer:

hope it help full

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Answer 2

Topic:-

Trigonometry

Question:-

$sin \theta = \frac{4}{5} \: then \: tan2 \theta \: =$

Solution:-

$First \:we \:know \:sin\theta= \dfrac{4}{5}$

$Now,\: find \:the\: value\: of \:tan\theta$

$We\: know \:that \:Sin \theta = \dfrac{opp}{hyp} \\ \\Tan\theta= \dfrac{Opp}{Adj} \\ \\So, tan\theta= \dfrac{4}{3} \\ We\: know \:that \:tan2\theta= \dfrac{2tan\theta}{1-tan²\theta} \\ \\ tan2\theta= \dfrac{2(\dfrac{4}{3})}{1-(\dfrac{4}{3})²}$

$tan2\theta= \dfrac{\dfrac{8}{3}}{1-(\dfrac{16}{9})}$

$tan2\theta= \dfrac{\dfrac{8}{3}}{\dfrac{9-16}{9}}$

$tan2\theta= \dfrac{\dfrac{8}{3}}{\dfrac{-7}{9}}$

$tan2\theta= \dfrac{8}{3}×\dfrac{9}{-7}$

$= \dfrac{24}{-7}$

Answer:-

$= \dfrac{24}{-7}$

More Information:-

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

Multiples:-

$sin2\theta= 2sin\theta cos\theta$

$sin2\theta=\dfrac{2tan\theta}{1+tan²\theta}$

$cos2\theta= cos²\theta-sin²\theta$

$cos2\theta= 1-2sin²\theta$

$cos2\theta= 2cos²\theta-1$

$cos2\theta= \dfrac{1-tan²\theta}{1+tan²\theta}$

$tan2\theta= \dfrac{2tan\theta}{1-tan²\theta}$

$cot2\theta= \dfrac{cot²\theta-1}{2cot\theta}$