Question

The value of tan-1{cos[pi/3]-sin[pi/3]/cos[pi/3]+sin[pi/3]} is

Answer 1

Answer:

π/12 + nπ

Step-by-step explanation:

tan-1{cos[pi/3]-sin[pi/3]/cos[pi/3]+sin[pi/3]}

= tan-1{cos60-sin60/cos 60+sin 60}

= tan-1{1/2-√3/2÷ 1/2+√3/2}

= tan-1{1-√3÷ 1+√3}

= tan-1{1-√3}²÷ -2

= tan-1{4-2√3}÷ -2

= tan-1{-2+√3}

= pi/12 + npi

= π/12 + nπ , n is a positive integer