Question

Solve cot x tan =___​

Answer 1

Question:

$solve \: \cot \alpha \times \tan\alpha =$

To Find:

$\cot \alpha \times \tan \alpha$

Solution:

$we \: can \: write \: \cot\alpha \: as \: \frac{ \cos( \alpha ) }{ \sin( \alpha ) }$

$we \: can \: also \: write \: \tan( \alpha ) as \: \frac{ \sin( \alpha ) }{ \cos( \alpha ) }$

So, Substitute those value in

$\cot \alpha \times tan \alpha$

$\frac{ \cos( \alpha ) }{ \sin( \alpha ) } \times \ \frac{ \sin( \alpha ) }{ \cos( \alpha ) ) }$

Then

$\cos( \alpha ) and \cos( \alpha ) will \: be \: cancelled \: and \: also \: \sin( \alpha ) and \sin( \alpha ) will \: cancelled \\ \\ \\ totally \: we \: get \: answer \: 1$

Answer:

$\cos( \alpha ) \times \tan( \alpha ) = 1$

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