Question

tan70theta -cot (500° - 3 0°)theta​

Answer 1

Answer:

tan70theta-cot(500-30)theta

Step-by-step explanation:

= tan70theta - cot 470theta

= tan70theta - cot(360+110)theta

= tan70theta - (-cot110theta)

= tan70theta + cot110theta

= tan70theta + cot(90+20)theta

= tan70theta -tan20theta

$tan(A-B)=\frac{tanA-tanB}{1+tanAtanB}\\tanA-tanB=tan(A-B).(1+tan AtanB)$

tan70theta - tan20theta=tan(70-20).(1+tan70.tan20)

tan70theta - tan20theta= tan50.(1+tan(90-20).tan20)

tan70theta - tan20theta = tan50.(1+cot20.tan20)   (cot(theta).tan(theta)=1)    

tan70theta - tan20theta = tan50(1+1)

tan70theta - tan20theta = tan50(2)

tan70theta - tan20theta = 2(1)

tan70theta - tan20theta=2

tan70theta=cot(500-30)theta=2