Q7 of 186 Page 332

Prove each of the following identities:
sin θ (1 + tan θ) + cos θ (1+ cot θ) = (sec θ + cosec θ)

Consider the left – hand side:

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

= sin θ (1 + ) + cos θ (1+ )

= sin θ × (cos θ) ×

= (cos θ + sin θ)

= cosec θ + sec θ

= R.H.S.

Hence, proved.

Prove each of the following identities:

sec θ(1 – sin θ)(sec θ + tan θ) = 1

Prove each of the following identities:

Prove each of the following identities:sin θ (1 + tan θ) + cos θ (1+ cot θ) = (sec θ + cosec θ)