Question

Tan(A+30)+Cot(A-30)​

Answer 1

Tan (A+30°) +Cot (A-30°) = 1/Sin2a-Sin60°

Explaination:

tan(a+30) +cot(a+30)

= sin(a+30)/cos(a+30) + cos(a-30)/sin(a-30)

taking LCM

= sin(a+30)sin(a-30) + cos(a+30)cos(a-30)/cos(a+30)sin(a-30)

using cosAcosB+sinAsinB = cos(A-B) (in numerator)

= cos(a+30 - (a-30))/cos(a+30)sin(a-30)

= cos(60)/cos(a+30)sin(a-30)

putting cos60=1/2

= 1/2cos(a+30)sin(a-30)

but 2cosAsinB = sin2A - sin2B

= 1/sin2a - sin2(30)

= 1/sin2a - sin60