Question

Prove that sin θ ( 1 – tan θ ) − cos θ ( 1 − cot θ ) = cosec θ − sec θ

Answer 1

Step-by-step explanation:

L.H.S. = sin θ (1 - tan θ) - cos θ (1- cot θ)

= sin θ (1 - sin θ/cos θ) - cos θ (1- cos θ/sinθ)

= sin θ{(cosθ -sinθ )/cos θ} - cos θ{(sinθ-cosθ )/sinθ}

=(cos θ - sin θ) (sinθ/cos θ - cos θ/sinθ)

= (cos θ - sin θ)/cos θ sin θ

= cosec θ - sec θ

= R.H.S.

Answer 2

$\huge \mathcal \colorbox{lightpink}{{Solution:}}$

$L:H:S = \sin0(1 + \tan0 ) + \cos0(1 + \cot0)$

$= \sin0(1 + \frac{ \sin0 }{cos0} ) + cos0(1 + \frac{ \cos0 }{sin0} )$

$= (sin0 + cos0)( \frac{sin0}{cos0} + \frac{cos0}{sin0} )$

$= \frac{(sin0 + cos0)}{sin0 \: cos0} ( {sin}^{2} 0 + {cos}^{2}0)$

$= ( \frac{1}{cos0} + \frac{1}{sin0} )$

$sec0 + cosec0 = R:H:S(proved)$

❥ the above is the answer of your question

❥ hope that's helps you