Question

show that root of 1 + sin a by 1 minus Sin A is equals to secant a + tan a​

Answer 1

Answer:

It is proved. See the attachment

Answer 2

Topic:-

Trigonometry

Question:-

$prove \: that \: \sqrt{ \dfrac{1 + sin \alpha }{1 - sin \alpha } } = sec \alpha + tan \alpha$

Solution:-

Now take LHS to prove

$\sqrt{ \frac{1 + sin \alpha }{1 - sin \alpha } }$

Now do rationalization

$\sqrt{ \frac{1 + sin \alpha }{1 - sin \alpha } \times \frac{1 + sin \alpha }{1 + sin \alpha } }$

$= \sqrt{ \frac{ {(1 + sin \alpha )}^{2} }{(1 + sin \alpha )(1 - si n \alpha )} }$

$\sqrt{ \frac{ {(1 + sin \alpha )}^{2} }{1 - {sin}^{2} \alpha } }$

$\sqrt{ \frac{ {(1 + sin \alpha )}^{2} }{ {cos}^{2} \alpha } }$

$\sqrt{ \frac{ {(1 + sin \alpha )}^{2} }{ {cos}^{2} \alpha } }$

$\sqrt{ (\frac{1 + sin \alpha }{cos \alpha } {)}^{2} }$

$\frac{1 + sin \alpha }{cos \alpha }$

$= \frac{1}{cos \alpha } + \frac{sin \alpha }{ \cos \alpha }$

$sec \alpha + tan \alpha$

Hence Proved //

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