Question

sino (t+tang )+ coso (It cotol =
(secot coseco).​

Answer 1

Step-by-step explanation:

we have to prove :

sinΦ(1+tanΦ)+cosΦ(1+cotΦ)

= (secΦ + cosecΦ)

LHS =( sinΦ)(1+[sinΦ/cosΦ])

+cosΦ(1+[cosΦ/sinΦ])

={(sinΦ)[(cosΦ+sinΦ)/(cosΦ)]}

+{cosΦ[(sinΦ+cosΦ)/(sinΦ)]}

={sin²Φ(cosΦ+sinΦ)+cos²Φ(sinΦ+cosΦ)}/(cosΦxsinΦ)

={(sin²Φ+cos²Φ)(cosΦ+sinΦ)}/(sinΦ.cosΦ)

=(cosΦ+sinΦ)/(sinΦ.cosΦ)

={(cosΦ)/(sinΦ.cosΦ)}+{(sinΦ)/(sinΦ.cosΦ)}

= (1/sinΦ) + (1/cosΦ)

= cosecΦ + secΦ = secΦ+cosecΦ

= RHS , hence proved