Question

Prove the following trigonometrici identity
tan²theta × cos²theta = 1-cos²theta​

Answer 1

Step-by-step explanation:

Your answer is here

We can write tan^theta as sec^theta-1

Answer 2

Topic:-

Trigonometry

Question:-

${tan}^{2} \theta \times {cos}^{2} \theta = 1 - co {s}^{2} \theta \: \\ prove \: it$

Solution:-

$taking \: lhs \\ \\ we \: know \: that \: \: \\ \\ {tan}^{2} \theta = {sec}^{2} \theta - 1 \\ \\ so \\ =( {sec}^{2} \theta - 1) \times {cos}^{2} \theta \\ \\ = {sec}^{2} \theta \times {cos}^{2} \theta - {cos}^{2} \theta \\ \\ = \frac{1}{ { \cancel{cos}^{2} \theta }} \times \cancel{co {s}^{2} \theta} - {cos }^{2} \theta \\ \\ = 1 - {cos}^{2} \theta \\ \\ hence \: proved$

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