Simplify the following: It can be written as

Simplify the following:

…………………..

Answer :

(i) It can be written as

= cos θ/cos θ + sin θ/cosec θ – 3 tan² 30⁰

= 1 + (sin θ × sin θ) – 3 (1/√3)²

= sin² θ + 1 – (3 × 1/3)

= sin² θ + 1 – 1

= sin² θ

(ii) It can be written as

= (sec θ cos θ tan θ)/(sin θ cosec θ tan θ) + cot θ/cot θ

So we get

= sec θ cos θ/sin θ cosec θ + 1

= 1/1 + 1

= 1 + 1

= 2

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