Question

prove that 1 minus sin square theta upon 1 + cot theta minus cos square theta upon 1 + tan theta equals to sin cos​

Answer 1

Answer:

Step-by-step explanation:

 1 - sin²θ/1 + cotθ - cos²θ/1 + tanθ

= (sin²θ + cos²θ) - sin²θ.tanθ/tanθ+ 1 - cos²θ/1 + tanθ

= (sin²θ + cos²θ)(tanθ+ 1) - sin²θ.tanθ - cos²θ / 1 + tanθ

= sin²θtanθ + cos²θtanθ +sin²θ + cos²θ - sin²θ.tanθ - cos²θ / 1 + tanθ

=  cos²θtanθ +sin²θ / 1 + tanθ

= cos³θtanθ + sin²θcosθ / cosθ + sinθ

= cos³θ (sinθ/cosθ) + sin²θcosθ / cosθ + sinθ  

= cos²θsinθ + sin²θcosθ/cosθ + sinθ

= cosθsinθ(cosθ + sinθ)/cosθ + sinθ

= cosθsinθ

= R.H.S

Hence proved.